EQUADIFF 6. Jean-Claude Nédélec Mixed finite element in 3D in H(div) and H(curl) Terms of use:
|
|
- Marvin Paul
- 6 years ago
- Views:
Transcription
1 EQUADIFF 6 Jean-Claude Nédélec Mixed finite element in 3D in H(div) and H(curl) In: Jaromír Vosmanský and Miloš Zlámal (eds.): Equadiff 6, Proceedings of the International Conference on Differential Equations and Their Applications held in Brno, Czechoslovakia, Aug , J. E. Purkyně University, Department of Mathematics, Brno, pp. [321] Persistent URL: Terms of use: Masaryk University, 1986 Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library
2 MIXED FINITE ELEMENT IN 3D IN H(div) AND H(curl) J. C NEDELEC Ecole Poly technique, Centre de Mathematiques Palaiseau, France Appliquees I. INTRODUCTION. Frayes De Venbeke first introduces the mixed finite element. Then P.A. Raviart and J.M. Thomas does some mathematics on these element in 2D and others do also : F. Brezzi V. Babuska... In 1980 we introduce a family of some mixed finite element in 3D and we use them for solving Navier Stokes equations. In 1984 F- Brezzi, J. Douglass and L.D. Marini introduce in 2D a new family of mixed finite element conforming in H(div). That paper was the starting point for building new families of finite element in 3D. II. FINITE ELEMENT IN H(div). Notations. K is a tetrahedron 3K its boundary n the normal f a face which area is f d y. r a is an edge which lenght is ds 'a curl u = V^ u u = (u, u, u~) H(curl) = {u e L 2 (Q)) 3 ; curl u G (L 2 (ft)) 3 } div V«u H(div) = {u (L 2 (ft)) 3 ; div u e L 2 (fi) } Spaces of polynomials. P = polynomials of degree less or equal to k homogeneous of degree k \ ' (I W 3 ~» + P k-1 - ' " 1 ~2 3 S k = {p Є (P^) ; (r.p) s 0 } ^k " (P k-l )3 Ф S k
3 322 dim S = k(k + 2) A- n - (k - 3)(k 1!) k dim v, ^ k 2,. 0 _ (k _ 3)(k + 2) k dim K. k 2 We are now able to introduce the finite element conforming in H(div). Definition. We define the finite element by 1) K is a tetrahedron 3 2) P = (P ) is a space of polynomials 3) The set of degrees of freedom which are (3.0 (p n)q dy ; V q P^f) ; f (3.2) j (p. q) dx ; V q G R fc_,. we have the Theorem. K The above finite element is unisolventand conforming in H(div). The associate interpolation operator II is such that div Tip = II* div p ; V p e H(div), * 2 where II is the L projection on P,.. k-1 When k = 1, the corresponding element has no interior moments and 12 degrees of freedom. Its divergence is constant. Proposition.For a tetrahedron "regular enough" which diameter is k, we have 11 P " " P "(L-(K))3 * C hk+ ' Mp "(Hk+l(K))3 i II D(p - n P) ll a2(k))3 < c h k llpll (Hk +l (K))3 We are not going to prove this theorem. But we can recall that a finite element is said to be conforming in a functional space if the interpolate of an element of this space belong to this space. In our case, the conformity in H(div) is equivalent to the continuity of the normal composent at each interface. This property is clearly true for our finite element since the unknowns on the face are J (p. n) q dy ; VqG P k (f) and p.n is also P, (f).
4 323 III. FINITE ELEMENT IN H(curl). A finite element is conforming in H(curl) if the tangential components are continue at the interface of the mesh. We introduce the corresponding finite element. Definition. 1) K is a tetrahedron 2) P = (P.) is the space of polynomials 3) The degrees of freedom are the following moments 3.1) I (p. T) q ds ; V q P^a) ^a 3.2) (p. q) dy ; V q G v (f) and tangent to the face f 3.3) (p. q) dx ; V q e V^_ 2. We have the Theorem. The above finite element is unisolvent and conforming in H(curl). Moreover if II is the corresponding interpolation operator andii the interpolation operator associate to the H(div) finite element introduce previously for degree k-1 we have curl lip = IT curl p IV. APPLICATION TO THE EQUATION OF STOKES. The Stokes'equation is usually written in the (u,p) variable in a bounded domain 3 Q of R as - V Au + grad p = f, in ft div u = 0 ul r = 0 We introduce the vector potential <J> as in ft - A<J> = curl u, in ft div (J> = 0, in ft <(> An r = 0 Then the Stokes equation can be written in the (4>,w) variables where We introduce a) = curl u H(div ) = { v Є (L 2 (ft)) 3 ; div v Є 0, v.n г = 0 } H = { ф e H(curl) ; div ф = 0 ; фanl = 0 }
5 324 I'hen a variational formulation of the Stokes equation is v (curl w.curl ij/)dx = (f.curl ip)dx ; V ^ G H k hi (w.il)dx - (curl $.curl n)dx = 0 ; V II G H(curl) hi hi Let C be a mesh covering Q. We can introduce some finite element spaces W v = { UK G H(curl) ; w., G (P. ) 3 ; V K G C } h h hi k k W = {u>, G W, ; w /s n I r = 0 } h h h h ' I V, = { v, e H(div) ; v,, G (p ) 3 ; V K G C } h h h k-1 h u = v n H(div ) h h The approximate problem become then v (curl w,.v, )dx = (f.v, )dx ; V v G n ; \ Q h h J^ h h h hi (w._.n, h h )dx - (u.curl IT) dx = 0 ; V II G W, k h h h h We can also use a vector potential (j),. This goes like that We have the Theorem. e h - { e h e B '(fl) ; e h ep k+, ; v K ec h > e - e h n H> K If the transgulation is regular,for every v G U,there exist a unique ik G W, such that r h h f curl ik = v, h h and we have also v 0 % * rad e h )dx < v 9 h e e h r h H(curl) h (L z (ft))-3 This theorem can be use to transfer the above approximate problem in one in (\jj,w) and also to find a local basis in the space U,
6 325 BIBLIOGRAPHY F. BREZZI, On the existence, uniqueness and approximation of saddle point problems ausing from Lagrangian multipliers. RAIRO 8 : (1974). F. BREZZI, J. DOUGLASS & L.D. MARINI, Two families of mixed finite elements for second order elliptic problems. To appear in Numerische Mathematik. P.G. CIARLET, The finite i-u-ment method for elliptic problems. North Holland Amsterdam (1978). P.G. CIARLET & P.A. RAVIART, A mixed finite element method for the biharmonic equation. Mathematical aspects in finite element method (C de Boor ed.) pp Academic Press New York (1974). M. FORTIN, An analysis of the convergence of mixed finite element method. RAIRO 11 : (1977). J.C. NEDELEC, Mixed finite element in ]R 3. Numerische Mathematik 35 : (1980). J.C. NEDELEC, Elements finis mixtes incompressibles pour 1'equation de Stokes dans (R 3. Numerische Mathematik 39, (1982). P.A. RAVIART & J.M. THOMAS, A mixed finite element method for 2nd order elliptic problems. In Dold A Eckmann B (eds) f Mathematical aspects of finite element methods. Lecture Notes 606 Springer Berlin (1977). J.M. THOMAS, Thesis Paris (1977). J.C. NEDELEC, A new family of mixed finite element in IR 3 (a paraitre).
Lecture Note III: Least-Squares Method
Lecture Note III: Least-Squares Method Zhiqiang Cai October 4, 004 In this chapter, we shall present least-squares methods for second-order scalar partial differential equations, elastic equations of solids,
More informationMixed Finite Element Methods. Douglas N. Arnold, University of Minnesota The 41st Woudschoten Conference 5 October 2016
Mixed Finite Element Methods Douglas N. Arnold, University of Minnesota The 41st Woudschoten Conference 5 October 2016 Linear elasticity Given the load f : Ω R n, find the displacement u : Ω R n and the
More informationA mixed finite element approximation of the Stokes equations with the boundary condition of type (D+N)
wwwijmercom Vol2, Issue1, Jan-Feb 2012 pp-464-472 ISSN: 2249-6645 A mixed finite element approximation of the Stokes equations with the boundary condition of type (D+N) Jaouad El-Mekkaoui 1, Abdeslam Elakkad
More informationError estimates for the Raviart-Thomas interpolation under the maximum angle condition
Error estimates for the Raviart-Thomas interpolation under the maximum angle condition Ricardo G. Durán and Ariel L. Lombardi Abstract. The classical error analysis for the Raviart-Thomas interpolation
More informationENERGY NORM A POSTERIORI ERROR ESTIMATES FOR MIXED FINITE ELEMENT METHODS
ENERGY NORM A POSTERIORI ERROR ESTIMATES FOR MIXED FINITE ELEMENT METHODS CARLO LOVADINA AND ROLF STENBERG Abstract The paper deals with the a-posteriori error analysis of mixed finite element methods
More informationMATH 676. Finite element methods in scientific computing
MATH 676 Finite element methods in scientific computing Wolfgang Bangerth, Texas A&M University Lecture 33.25: Which element to use Part 2: Saddle point problems Consider the stationary Stokes equations:
More informationarxiv: v1 [math.na] 27 Jan 2016
Virtual Element Method for fourth order problems: L 2 estimates Claudia Chinosi a, L. Donatella Marini b arxiv:1601.07484v1 [math.na] 27 Jan 2016 a Dipartimento di Scienze e Innovazione Tecnologica, Università
More informationAMS subject classifications. Primary, 65N15, 65N30, 76D07; Secondary, 35B45, 35J50
A SIMPLE FINITE ELEMENT METHOD FOR THE STOKES EQUATIONS LIN MU AND XIU YE Abstract. The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in
More informationarxiv: v1 [math.na] 27 Jan 2016
Virtual Element Method for fourth order problems: L 2 estimates Claudia Chinosi a, L. Donatella Marini b arxiv:1601.07484v1 [math.na] 27 Jan 2016 a Dipartimento di Scienze e Innovazione Tecnologica, Università
More informationEXISTENCE AND REGULARITY OF SOLUTIONS FOR STOKES SYSTEMS WITH NON-SMOOTH BOUNDARY DATA IN A POLYHEDRON
Electronic Journal of Differential Equations, Vol. 2017 (2017), No. 147, pp. 1 10. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu EXISTENCE AND REGULARITY OF SOLUTIONS FOR
More informationFinite element approximation on quadrilateral meshes
COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Commun. Numer. Meth. Engng 2001; 17:805 812 (DOI: 10.1002/cnm.450) Finite element approximation on quadrilateral meshes Douglas N. Arnold 1;, Daniele
More informationNumerische Mathematik
Numer. Math. (2003) 94: 195 202 Digital Object Identifier (DOI) 10.1007/s002110100308 Numerische Mathematik Some observations on Babuška and Brezzi theories Jinchao Xu, Ludmil Zikatanov Department of Mathematics,
More informationA P4 BUBBLE ENRICHED P3 DIVERGENCE-FREE FINITE ELEMENT ON TRIANGULAR GRIDS
A P4 BUBBLE ENRICHED P3 DIVERGENCE-FREE FINITE ELEMENT ON TRIANGULAR GRIDS SHANGYOU ZHANG DEDICATED TO PROFESSOR PETER MONK ON THE OCCASION OF HIS 6TH BIRTHDAY Abstract. On triangular grids, the continuous
More informationFinite element exterior calculus: A new approach to the stability of finite elements
Finite element exterior calculus: A new approach to the stability of finite elements Douglas N. Arnold joint with R. Falk and R. Winther Institute for Mathematics and its Applications University of Minnesota
More informationMODEL OF GROUNDWATER FLOW IN FRACTURED ENVIRONMENT
Proceedings of ALGORITMY 2002 Conference on Scientific Computing, pp. 138 145 MODEL OF GROUNDWATER FLOW IN FRACTURED ENVIRONMENT JIŘÍ MARYŠKA, OTTO SEVERÝN AND MARTIN VOHRALÍK Abstract. A stochastic discrete
More informationError analysis for a new mixed finite element method in 3D
Trabalho apresentado no CNMAC, Gramado - RS, 2016. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics Error analysis for a new mixed finite element method in 3D Douglas
More informationUne méthode de pénalisation par face pour l approximation des équations de Navier-Stokes à nombre de Reynolds élevé
Une méthode de pénalisation par face pour l approximation des équations de Navier-Stokes à nombre de Reynolds élevé CMCS/IACS Ecole Polytechnique Federale de Lausanne Erik.Burman@epfl.ch Méthodes Numériques
More informationArchivum Mathematicum
Archivum Mathematicum Miloš Háčik Contribution to the monotonicity of the sequence of zero points of integrals of the differential equation y + g(t)y = 0 with regard to the basis [α, β] Archivum Mathematicum,
More informationDivergence-free or curl-free finite elements for solving the curl-div system
Divergence-free or curl-free finite elements for solving the curl-div system Alberto Valli Dipartimento di Matematica, Università di Trento, Italy Joint papers with: Ana Alonso Rodríguez Dipartimento di
More informationSTABILIZED DISCONTINUOUS FINITE ELEMENT APPROXIMATIONS FOR STOKES EQUATIONS
STABILIZED DISCONTINUOUS FINITE ELEMENT APPROXIMATIONS FOR STOKES EQUATIONS RAYTCHO LAZAROV AND XIU YE Abstract. In this paper, we derive two stabilized discontinuous finite element formulations, symmetric
More informationA Mixed Nonconforming Finite Element for Linear Elasticity
A Mixed Nonconforming Finite Element for Linear Elasticity Zhiqiang Cai, 1 Xiu Ye 2 1 Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395 2 Department of Mathematics and Statistics,
More informationFEniCS Course. Lecture 0: Introduction to FEM. Contributors Anders Logg, Kent-Andre Mardal
FEniCS Course Lecture 0: Introduction to FEM Contributors Anders Logg, Kent-Andre Mardal 1 / 46 What is FEM? The finite element method is a framework and a recipe for discretization of mathematical problems
More informationIntroduction to finite element exterior calculus
Introduction to finite element exterior calculus Ragnar Winther CMA, University of Oslo Norway Why finite element exterior calculus? Recall the de Rham complex on the form: R H 1 (Ω) grad H(curl, Ω) curl
More informationArchivum Mathematicum
Archivum Mathematicum Theodore Artikis Constructing infinitely divisible characteristic functions Archivum Mathematicum, Vol. 19 (1983), No. 2, 57--61 Persistent URL: http://dml.cz/dmlcz/107156 Terms of
More informationArchivum Mathematicum
Archivum Mathematicum Zdeněk Dušek; Oldřich Kowalski How many are affine connections with torsion Archivum Mathematicum, Vol. 50 (2014), No. 5, 257 264 Persistent URL: http://dml.cz/dmlcz/144068 Terms
More informationNONCONFORMING MIXED ELEMENTS FOR ELASTICITY
Mathematical Models and Methods in Applied Sciences Vol. 13, No. 3 (2003) 295 307 c World Scientific Publishing Company NONCONFORMING MIXED ELEMENTS FOR ELASTICITY DOUGLAS N. ARNOLD Institute for Mathematics
More informationH(div) and H(curl)-conforming Virtual Element Methods
Noname manuscript No. (will be inserted by the editor) H(div) and H(curl)-conforming Virtual Element Methods L. Beirão da Veiga F. Brezzi L. D. Marini A. Russo the date of receipt and acceptance should
More informationSolving the curl-div system using divergence-free or curl-free finite elements
Solving the curl-div system using divergence-free or curl-free finite elements Alberto Valli Dipartimento di Matematica, Università di Trento, Italy or: Why I say to my students that divergence-free finite
More informationČasopis pro pěstování matematiky
Časopis pro pěstování matematiky án Andres On stability and instability of the roots of the oscillatory function in a certain nonlinear differential equation of the third order Časopis pro pěstování matematiky,
More informationUniform inf-sup condition for the Brinkman problem in highly heterogeneous media
Uniform inf-sup condition for the Brinkman problem in highly heterogeneous media Raytcho Lazarov & Aziz Takhirov Texas A&M May 3-4, 2016 R. Lazarov & A.T. (Texas A&M) Brinkman May 3-4, 2016 1 / 30 Outline
More informationMotivations. Outline. Finite element exterior calculus and the geometrical basis of numerical stability. References. Douglas N.
Outline Finite element exterior calculus and the geometrical basis of numerical stability Douglas N. Arnold joint with R. Falk and R. Winther School of Mathematics University of Minnesota April 009 Motivations
More informationAplikace matematiky. Gene Howard Golub Numerical methods for solving linear least squares problems
Aplikace matematiky Gene Howard Golub Numerical methods for solving linear least squares problems Aplikace matematiky, Vol. 10 (1965), No. 3, 213--216 Persistent URL: http://dml.cz/dmlcz/102951 Terms of
More informationANDREA TOSELLI. Abstract. Two-level overlapping Schwarz methods are considered for nite element problems
OVERLAPPING SCHWARZ METHODS FOR MAXWELL'S EQUATIONS IN THREE DIMENSIONS ANDREA TOSELLI Abstract. Two-level overlapping Schwarz methods are considered for nite element problems of 3D Maxwell's equations.
More informationHEXAHEDRAL H(DIV) AND H(CURL) FINITE ELEMENTS
HEXAHEDRAL H(DIV) AND H(CURL) FINITE ELEMENTS RICHARD S. FAL, PAOLO GATTO, AND PETER MON Abstract. We study the approximation properties of some finite element subspaces of H(div; Ω) and H(curl ; Ω) defined
More informationENERGY NORM A POSTERIORI ERROR ESTIMATES FOR MIXED FINITE ELEMENT METHODS
MATHEMATICS OF COMPUTATION Volume 75, Number 256, October 2006, Pages 1659 1674 S 0025-57180601872-2 Article electronically published on June 26, 2006 ENERGY NORM A POSTERIORI ERROR ESTIMATES FOR MIXED
More informationFINITE ELEMENT APPROXIMATION OF STOKES-LIKE SYSTEMS WITH IMPLICIT CONSTITUTIVE RELATION
Proceedings of ALGORITMY pp. 9 3 FINITE ELEMENT APPROXIMATION OF STOKES-LIKE SYSTEMS WITH IMPLICIT CONSTITUTIVE RELATION JAN STEBEL Abstract. The paper deals with the numerical simulations of steady flows
More informationA SECOND ELASTICITY ELEMENT USING THE MATRIX BUBBLE WITH TIGHTENED STRESS SYMMETRY
A SECOND ELASTICITY ELEMENT USING THE MATRIX BUBBLE WITH TIGHTENED STRESS SYMMETRY J. GOPALAKRISHNAN AND J. GUZMÁN Abstract. We presented a family of finite elements that use a polynomial space augmented
More informationEQUADIFF 1. Rudolf Výborný On a certain extension of the maximum principle. Terms of use:
EQUADIFF 1 Rudolf Výborný On a certain extension of the maximum principle In: (ed.): Differential Equations and Their Applications, Proceedings of the Conference held in Prague in September 1962. Publishing
More informationSemi-discrete finite element approximation applied to Maxwell s equations in nonlinear media
Semi-discrete finite element approximation applied to Maxwell s equations in nonlinear media Lutz Angermann arxiv:9.365v math.na Jan 9 January 9, 9 In this paper the semi-discrete finite element approximation
More informationA MULTIGRID METHOD FOR THE PSEUDOSTRESS FORMULATION OF STOKES PROBLEMS
SIAM J. SCI. COMPUT. Vol. 29, No. 5, pp. 2078 2095 c 2007 Society for Industrial and Applied Mathematics A MULTIGRID METHOD FOR THE PSEUDOSTRESS FORMULATION OF STOKES PROBLEMS ZHIQIANG CAI AND YANQIU WANG
More informationActa Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica-Physica-Chemica
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica-Physica-Chemica Vladimír Janků The thermodynamical properties of an ideal gas in a periodical potential field Acta Universitatis
More informationCommentationes Mathematicae Universitatis Carolinae
Commentationes Mathematicae Universitatis Carolinae Bogdan Szal Trigonometric approximation by Nörlund type means in L p -norm Commentationes Mathematicae Universitatis Carolinae, Vol. 5 (29), No. 4, 575--589
More informationČasopis pro pěstování matematiky
Časopis pro pěstování matematiky Alois Švec Determination of a surface by its mean curvature Časopis pro pěstování matematiky, Vol. 103 (1978), No. 2, 175--180 Persistent URL: http://dml.cz/dmlcz/108617
More informationPARTITION OF UNITY FOR THE STOKES PROBLEM ON NONMATCHING GRIDS
PARTITION OF UNITY FOR THE STOES PROBLEM ON NONMATCHING GRIDS CONSTANTIN BACUTA AND JINCHAO XU Abstract. We consider the Stokes Problem on a plane polygonal domain Ω R 2. We propose a finite element method
More informationA NEW FAMILY OF STABLE MIXED FINITE ELEMENTS FOR THE 3D STOKES EQUATIONS
MATHEMATICS OF COMPUTATION Volume 74, Number 250, Pages 543 554 S 0025-5718(04)01711-9 Article electronically published on August 31, 2004 A NEW FAMILY OF STABLE MIXED FINITE ELEMENTS FOR THE 3D STOKES
More informationA variation on the infsup condition
Cinquième foire européenne aux éléments finis Centre International de Rencontres Mathématiques Marseille Luminy, 17-19 mai 2007 A variation on the infsup condition François Dubois CNAM Paris and University
More informationHigh Order Differential Form-Based Elements for the Computation of Electromagnetic Field
1472 IEEE TRANSACTIONS ON MAGNETICS, VOL 36, NO 4, JULY 2000 High Order Differential Form-Based Elements for the Computation of Electromagnetic Field Z Ren, Senior Member, IEEE, and N Ida, Senior Member,
More informationSTOKES PROBLEM WITH SEVERAL TYPES OF BOUNDARY CONDITIONS IN AN EXTERIOR DOMAIN
Electronic Journal of Differential Equations, Vol. 2013 2013, No. 196, pp. 1 28. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu STOKES PROBLEM
More informationDISCRETE HODGE HELMHOLTZ
Monografías Matemáticas García de Galdeano 39, 1 10 (2014) DISCRETE HODGE HELMHOLTZ DECOMPOSITION Etienne Ahusborde, Mejdi Azaïez, Jean-Paul Caltagirone, Mark Gerritsma and Antoine Lemoine Abstract. This
More informationb i (x) u + c(x)u = f in Ω,
SIAM J. NUMER. ANAL. Vol. 39, No. 6, pp. 1938 1953 c 2002 Society for Industrial and Applied Mathematics SUBOPTIMAL AND OPTIMAL CONVERGENCE IN MIXED FINITE ELEMENT METHODS ALAN DEMLOW Abstract. An elliptic
More informationOn the equivalence of regularity criteria for triangular and tetrahedral finite element partitions
Computers and Mathematics with Applications 55 (2008) 2227 2233 www.elsevier.com/locate/camwa On the equivalence of regularity criteria for triangular and tetrahedral finite element partitions Jan Brandts
More informationWSAA 14. A. K. Kwaśniewski Algebraic properties of the 3-state vector Potts model. Terms of use:
WSAA 14 A. K. Kwaśniewski Algebraic properties of the 3-state vector Potts model In: Zdeněk Frolík and Vladimír Souček and Marián J. Fabián (eds.): Proceedings of the 14th Winter School on Abstract Analysis.
More informationA primer on Numerical methods for elasticity
A primer on Numerical methods for elasticity Douglas N. Arnold, University of Minnesota Complex materials: Mathematical models and numerical methods Oslo, June 10 12, 2015 One has to resort to the indignity
More informationDivergence-conforming multigrid methods for incompressible flow problems
Divergence-conforming multigrid methods for incompressible flow problems Guido Kanschat IWR, Universität Heidelberg Prague-Heidelberg-Workshop April 28th, 2015 G. Kanschat (IWR, Uni HD) Hdiv-DG Práha,
More informationUnified Hybridization Of Discontinuous Galerkin, Mixed, And Continuous Galerkin Methods For Second Order Elliptic Problems.
Unified Hybridization Of Discontinuous Galerkin, Mixed, And Continuous Galerkin Methods For Second Order Elliptic Problems. Stefan Girke WWU Münster Institut für Numerische und Angewandte Mathematik 10th
More informationSymmetric Matrix Fields in the Finite Element Method
Symmetry 2010, 2, 1375-1389; doi:10.3390/sym2031375 OPEN ACCESS symmetry ISSN 2073-8994 www.mdpi.com/journal/symmetry Review Symmetric Matrix Fields in the Finite Element Method Gerard Awanou Northern
More informationarxiv: v1 [math.na] 3 Jun 2016
SRNDIPITY FAC AND DG VM SPACS L. BIRÃO DA VIGA[1], F. BRZZI [2], L.D. MARINI [3], A. RUSSO [1] arxiv:1606.01048v1 [math.na] 3 Jun 2016 Abstract. We extend the basic idea of Serendipity Virtual lements
More informationGlowinski Pironneau method for the 3D ω-ψ equations
280 GUERMOND AND QUARTAPELLE Glowinski Pironneau method for the 3D ω-ψ equations Jean-Luc Guermond and Luigi Quartapelle 1 LIMSI CNRS, Orsay, France, and Dipartimento di Fisica, Politecnico di Milano,
More informationAN ANALYSIS OF NEW FINITE ELEMENT SPACES FOR MAXWELL S EQUATIONS
Journal of Matematical Sciences: Advances and Applications Volume 5 8 Pages -9 Available at ttp://scientificadvances.co.in DOI: ttp://d.doi.org/.864/jmsaa_7975 AN ANALYSIS OF NEW FINITE ELEMENT SPACES
More informationDISCRETE EXTENSION OPERATORS FOR MIXED FINITE ELEMENT SPACES ON LOCALLY REFINED MESHES
DISCRETE EXTENSION OPERATORS FOR MIXED FINITE ELEMENT SPACES ON LOCALLY REFINED MESHES MAR AINSWORTH, JOHNNY GUZMÁN, AND FRANCISCO JAVIER SAYAS Abstract. The existence of uniformly bounded discrete extension
More informationA Petrov-Galerkin Enriched Method: A Mass Conservative Finite Element Method For The Darcy Equation
University of Colorado at Denver and Health Sciences Center A Petrov-Galerkin Enriched Method: A Mass Conservative Finite Element Method For The Darcy Equation Gabriel R. Barrenechea, Leopoldo P. Franca,
More informationLinear Differential Transformations of the Second Order
Linear Differential Transformations of the Second Order In: Otakar Borůvka (author); Felix M. Arscott (translator): Linear Differential Transformations of the Second Order. (English). London: The English
More informationA Stable Mixed Finite Element Scheme for the Second Order Elliptic Problems
A Stable Mixed Finite Element Scheme for the Second Order Elliptic Problems Miaochan Zhao, Hongbo Guan, Pei Yin Abstract A stable mixed finite element method (MFEM) for the second order elliptic problems,
More informationarxiv: v1 [math-ph] 25 Apr 2013
Higher-order compatible discretization on hexahedrals Jasper Kreeft and Marc Gerritsma arxiv:1304.7018v1 [math-ph] 5 Apr 013 Abstract We derive a compatible discretization method that relies heavily on
More informationA Second Elasticity Element Using the Matrix Bubble
Portland State University PDXScholar Mathematics and Statistics Faculty Publications and Presentations Fariborz Maseeh Department of Mathematics and Statistics 2011 A Second Elasticity Element Using the
More informationTwo-scale Dirichlet-Neumann preconditioners for boundary refinements
Two-scale Dirichlet-Neumann preconditioners for boundary refinements Patrice Hauret 1 and Patrick Le Tallec 2 1 Graduate Aeronautical Laboratories, MS 25-45, California Institute of Technology Pasadena,
More informationEQUADIFF 7. Linard Eduardovič Reizinš Theory of completely integrable equations. Terms of use:
EQUADIFF 7 Linard Eduardovič Reizinš Theory of completely integrable equations In: Jaroslav Kurzweil (ed.): Equadiff 7, Proceedings of the 7th Czechoslovak Conference on Differential Equations and Their
More informationCommentationes Mathematicae Universitatis Carolinae
Commentationes Mathematicae Universitatis Carolinae Pavel Drábek Remarks on multiple periodic solutions of nonlinear ordinary differential equations Commentationes Mathematicae Universitatis Carolinae,
More informationA posteriori error estimates applied to flow in a channel with corners
Mathematics and Computers in Simulation 61 (2003) 375 383 A posteriori error estimates applied to flow in a channel with corners Pavel Burda a,, Jaroslav Novotný b, Bedřich Sousedík a a Department of Mathematics,
More informationA posteriori error estimates for Maxwell Equations
www.oeaw.ac.at A posteriori error estimates for Maxwell Equations J. Schöberl RICAM-Report 2005-10 www.ricam.oeaw.ac.at A POSTERIORI ERROR ESTIMATES FOR MAXWELL EQUATIONS JOACHIM SCHÖBERL Abstract. Maxwell
More informationError analysis of piecewise constant approximations of Darcy s law
Error analysis of piecewise constant approximations of Darcy s law F. Brezzi 1,2, M. Fortin 3, L.D. Marini 1,2 January 17, 2005 Keywords Darcy, Finite Elements, Mixed formulations, Constant pressures,
More informationMIXED FINITE ELEMENT METHODS FOR PROBLEMS WITH ROBIN BOUNDARY CONDITIONS
MIXED FINITE ELEMENT METHODS FOR PROBLEMS WITH ROBIN BOUNDARY CONDITIONS JUHO KÖNNÖ, DOMINIK SCHÖTZAU, AND ROLF STENBERG Abstract. We derive new a-priori and a-posteriori error estimates for mixed nite
More informationFinite Elements for Magnetohydrodynamics and its Optimal Control
Finite Elements for Magnetohydrodynamics and its Karl Kunisch Marco Discacciati (RICAM) FEM Symposium Chemnitz September 25 27, 2006 Overview 1 2 3 What is Magnetohydrodynamics? Magnetohydrodynamics (MHD)
More informationA Multigrid Method for Two Dimensional Maxwell Interface Problems
A Multigrid Method for Two Dimensional Maxwell Interface Problems Susanne C. Brenner Department of Mathematics and Center for Computation & Technology Louisiana State University USA JSA 2013 Outline A
More informationQUADRILATERAL H(DIV) FINITE ELEMENTS
QUADRILATERAL H(DIV) FINITE ELEMENTS DOUGLAS N. ARNOLD, DANIELE BOFFI, AND RICHARD S. FALK Abstract. We consider the approximation properties of quadrilateral finite element spaces of vector fields defined
More informationOn an Approximation Result for Piecewise Polynomial Functions. O. Karakashian
BULLETIN OF THE GREE MATHEMATICAL SOCIETY Volume 57, 010 (1 7) On an Approximation Result for Piecewise Polynomial Functions O. arakashian Abstract We provide a new approach for proving approximation results
More informationHybrid Discontinuous Galerkin methods for incompressible flow problems
Hybrid Discontinuous Galerkin methods incompressible flow problems Christoph Lehrenfeld, Joachim Schöberl MathCCES Computational Mathematics in Engineering Workshop Linz, May 31 - June 1, 2010 Contents
More informationETNA Kent State University
Electronic Transactions on Numerical Analysis. Volume 11, pp. 1-24, 2000. Copyright 2000,. ISSN 1068-9613. ETNA NEUMANN NEUMANN METHODS FOR VECTOR FIELD PROBLEMS ANDREA TOSELLI Abstract. In this paper,
More informationA NOTE ON THE LADYŽENSKAJA-BABUŠKA-BREZZI CONDITION
A NOTE ON THE LADYŽENSKAJA-BABUŠKA-BREZZI CONDITION JOHNNY GUZMÁN, ABNER J. SALGADO, AND FRANCISCO-JAVIER SAYAS Abstract. The analysis of finite-element-like Galerkin discretization techniques for the
More informationMathematica Slovaca. Ján Jakubík On the α-completeness of pseudo MV-algebras. Terms of use: Persistent URL:
Mathematica Slovaca Ján Jakubík On the α-completeness of pseudo MV-algebras Mathematica Slovaca, Vol. 52 (2002), No. 5, 511--516 Persistent URL: http://dml.cz/dmlcz/130365 Terms of use: Mathematical Institute
More informationLINEAR FLOW IN POROUS MEDIA WITH DOUBLE PERIODICITY
PORTUGALIAE MATHEMATICA Vol. 56 Fasc. 2 1999 LINEAR FLOW IN POROUS MEDIA WITH DOUBLE PERIODICITY R. Bunoiu and J. Saint Jean Paulin Abstract: We study the classical steady Stokes equations with homogeneous
More informationPAijpam.eu NEW H 1 (Ω) CONFORMING FINITE ELEMENTS ON HEXAHEDRA
International Journal of Pure and Applied Mathematics Volume 109 No. 3 2016, 609-617 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v109i3.10
More informationMORTAR MULTISCALE FINITE ELEMENT METHODS FOR STOKES-DARCY FLOWS
MORTAR MULTISCALE FINITE ELEMENT METHODS FOR STOKES-DARCY FLOWS VIVETTE GIRAULT, DANAIL VASSILEV, AND IVAN YOTOV Abstract. We investigate mortar multiscale numerical methods for coupled Stokes and Darcy
More informationNedelec elements for computational electromagnetics
Nedelec elements for computational electromagnetics Per Jacobsson, June 5, 2007 Maxwell s equations E = jωµh () H = jωεe + J (2) (εe) = ρ (3) (µh) = 0 (4) J = jωρ (5) Only three of the equations are needed,
More informationDiscontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications Paola. Antonietti MOX, Dipartimento di Matematica Politecnico di Milano.MO. X MODELLISTICA E CALCOLO SCIENTIICO. MODELING AND SCIENTIIC
More informationLocal flux mimetic finite difference methods
Local flux mimetic finite difference methods Konstantin Lipnikov Mikhail Shashkov Ivan Yotov November 4, 2005 Abstract We develop a local flux mimetic finite difference method for second order elliptic
More informationCzechoslovak Mathematical Journal
Czechoslovak Mathematical Journal Garyfalos Papaschinopoulos; John Schinas Criteria for an exponential dichotomy of difference equations Czechoslovak Mathematical Journal, Vol. 35 (1985), No. 2, 295 299
More informationA DELTA-REGULARIZATION FINITE ELEMENT METHOD FOR A DOUBLE CURL PROBLEM WITH DIVERGENCE-FREE CONSTRAINT
A DELTA-REGULARIZATION FINITE ELEMENT METHOD FOR A DOUBLE CURL PROBLEM WITH DIVERGENCE-FREE CONSTRAINT HUOYUAN DUAN, SHA LI, ROGER C. E. TAN, AND WEIYING ZHENG Abstract. To deal with the divergence-free
More informationMultigrid Methods for Saddle Point Problems
Multigrid Methods for Saddle Point Problems Susanne C. Brenner Department of Mathematics and Center for Computation & Technology Louisiana State University Advances in Mathematics of Finite Elements (In
More informationMathematica Bohemica
Mathematica Bohemica Cristian Bereanu; Jean Mawhin Existence and multiplicity results for nonlinear second order difference equations with Dirichlet boundary conditions Mathematica Bohemica, Vol. 131 (2006),
More informationMathematica Bohemica
Mathematica Bohemica Radomír Halaš Remarks on commutative Hilbert algebras Mathematica Bohemica, Vol. 127 (2002), No. 4, 525--529 Persistent URL: http://dml.cz/dmlcz/133956 Terms of use: Institute of Mathematics
More informationDiscontinuous Galerkin Methods
Discontinuous Galerkin Methods Joachim Schöberl May 20, 206 Discontinuous Galerkin (DG) methods approximate the solution with piecewise functions (polynomials), which are discontinuous across element interfaces.
More informationEnergy norm a-posteriori error estimation for divergence-free discontinuous Galerkin approximations of the Navier-Stokes equations
INTRNATIONAL JOURNAL FOR NUMRICAL MTHODS IN FLUIDS Int. J. Numer. Meth. Fluids 19007; 1:1 [Version: 00/09/18 v1.01] nergy norm a-posteriori error estimation for divergence-free discontinuous Galerkin approximations
More informationwith Applications to Elasticity and Compressible Flow Daoqi Yang March 20, 1997 Abstract
Stabilized Schemes for Mixed Finite Element Methods with Applications to Elasticity and Compressible Flow Problems Daoqi Yang March 20, 1997 Abstract Stabilized iterative schemes for mixed nite element
More informationVirtual Element Methods for general second order elliptic problems
Virtual Element Methods for general second order elliptic problems Alessandro Russo Department of Mathematics and Applications University of Milano-Bicocca, Milan, Italy and IMATI-CNR, Pavia, Italy Workshop
More informationSUPERCONVERGENCE PROPERTIES FOR OPTIMAL CONTROL PROBLEMS DISCRETIZED BY PIECEWISE LINEAR AND DISCONTINUOUS FUNCTIONS
SUPERCONVERGENCE PROPERTIES FOR OPTIMAL CONTROL PROBLEMS DISCRETIZED BY PIECEWISE LINEAR AND DISCONTINUOUS FUNCTIONS A. RÖSCH AND R. SIMON Abstract. An optimal control problem for an elliptic equation
More informationMathematica Bohemica
Mathematica Bohemica Vinayak V. Joshi; B. N. Waphare Characterizations of 0-distributive posets Mathematica Bohemica, Vol. 130 (2005), No. 1, 73 80 Persistent URL: http://dml.cz/dmlcz/134222 Terms of use:
More informationA local-structure-preserving local discontinuous Galerkin method for the Laplace equation
A local-structure-preserving local discontinuous Galerkin method for the Laplace equation Fengyan Li 1 and Chi-Wang Shu 2 Abstract In this paper, we present a local-structure-preserving local discontinuous
More informationOverlapping Schwarz Preconditioners for Spectral. Problem in H(curl)
Overlapping Schwarz Preconditioners for Spectral Nédélec Elements for a Model Problem in H(curl) Technical Report TR2002-83 November 22, 2002 Department of Computer Science Courant Institute of Mathematical
More informationFinite Element Modeling of Electromagnetic Systems
Finite Element Modeling of Electromagnetic Systems Mathematical and numerical tools Unit of Applied and Computational Electromagnetics (ACE) Dept. of Electrical Engineering - University of Liège - Belgium
More information