We propose an approximation of the solution of the biharmonic problem in which relies on the discretization of the Laplace operator using nonconforming continuous piecewise linear finite elements.
Nous proposons une approximation de la solution du problème bi-harmonique dans basée sur la discrétisation du Laplacien par éléments finis P1 continus mais non conformes.
Accepted:
Published online:
Robert Eymard 1; Raphaèle Herbin 2
@article{CRMATH_2010__348_23-24_1283_0, author = {Robert Eymard and Rapha\`ele Herbin}, title = {Approximation of the biharmonic problem using piecewise linear finite elements}, journal = {Comptes Rendus. Math\'ematique}, pages = {1283--1286}, publisher = {Elsevier}, volume = {348}, number = {23-24}, year = {2010}, doi = {10.1016/j.crma.2010.11.002}, language = {en}, }
TY - JOUR AU - Robert Eymard AU - Raphaèle Herbin TI - Approximation of the biharmonic problem using piecewise linear finite elements JO - Comptes Rendus. Mathématique PY - 2010 SP - 1283 EP - 1286 VL - 348 IS - 23-24 PB - Elsevier DO - 10.1016/j.crma.2010.11.002 LA - en ID - CRMATH_2010__348_23-24_1283_0 ER -
Robert Eymard; Raphaèle Herbin. Approximation of the biharmonic problem using piecewise linear finite elements. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1283-1286. doi : 10.1016/j.crma.2010.11.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.002/
[1] A compact difference scheme for the biharmonic equation in planar irregular domains, SIAM J. Numer. Anal., Volume 47 (2009) no. 4, pp. 3087-3108
[2] A fast direct solver for the biharmonic problem in a rectangular grid, SIAM J. Sci. Comput., Volume 31 (2008) no. 1, pp. 303-333
[3] Mortar finite volume method with Adini element for biharmonic problem, J. Comput. Math., Volume 22 (2004) no. 3, pp. 475-488
[4] C0 interior penalty methods for fourth order elliptic boundary value problems on polygonal domains, J. Sci. Comput., Volume 22/23 (2005), pp. 83-118
[5] Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991
[6] A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow, Adv. Comput. Math., Volume 29 (2008) no. 2, pp. 113-133
[7] The finite element method (P.G. Ciarlet; J.-L. Lions, eds.), Handbook of Numerical Analysis, vol. III, Part I, North-Holland, Amsterdam, 1991
[8] Mathematical Analysis of Thin Plate Models, Mathématiques & Applications [Mathematics & Applications], vol. 24, Springer-Verlag, Berlin, 1996
[9] R. Eymard, T. Gallouët, Herbin, Finite volume schemes for the biharmonic problem on general meshes, 2010, submitted for publication.
[10] Discontinuous Galerkin methods for the biharmonic problem, IMA J. Numer. Anal., Volume 29 (2009) no. 3, pp. 573-594
[11] Mixed discontinuous Galerkin finite element method for the biharmonic equation, J. Sci. Comput., Volume 37 (2008) no. 2, pp. 139-161
[12] hp-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation, J. Sci. Comput., Volume 30 (2007) no. 3, pp. 465-491
[13] hp-version interior penalty DGFEMs for the biharmonic equation, Comput. Methods Appl. Mech. Engrg., Volume 196 (2007) no. 13–16, pp. 1851-1863
[14] A mixed finite volume element method based on rectangular mesh for biharmonic equations, J. Comput. Appl. Math., Volume 172 (2004) no. 1, pp. 117-130
Cited by Sources:
Comments - Policy