Discontinuous Galerkin methods handle very well general polygonal and nonmatching meshes. We present in this Note a -conforming reconstruction of the flux on such meshes in the setting of an elliptic problem. We exploit the local conservation property of discontinuous Galerkin methods and solve local Neumann problems by means of the Raviart–Thomas–Nédélec mixed finite element method. Our reconstruction can be used in a guaranteed a posteriori error estimate and it is also of independent interest when the approximate flux is to be used subsequently in a transport problem.
Les méthodes de Galerkine discontinues sont bien adaptées pour traiter des maillages non-coïncidants avec mailles polygonales. Nous présentons dans cette Note une reconstruction -conforme du flux sur de tels maillages pour un problème elliptique. Nous exploitons la propriété de conservativité locale des méthodes de Galerkine discontinues afin de résoudre des problèmes locaux de Neumann approchés par des éléments finis mixtes de Raviart–Thomas–Nédélec. Notre reconstruction peut être utilisée pour une estimation garantie d'erreur a posteriori et également afin d'évaluer une vitesse approchée pour un problème de transport.
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@article{CRMATH_2009__347_7-8_441_0, author = {Ern, Alexandre and Vohral{\'\i}k, Martin}, title = {Flux reconstruction and a posteriori error estimation for discontinuous {Galerkin} methods on general nonmatching grids}, journal = {Comptes Rendus. Math\'ematique}, pages = {441--444}, publisher = {Elsevier}, volume = {347}, number = {7-8}, year = {2009}, doi = {10.1016/j.crma.2009.01.017}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.01.017/} }
TY - JOUR AU - Ern, Alexandre AU - Vohralík, Martin TI - Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids JO - Comptes Rendus. Mathématique PY - 2009 SP - 441 EP - 444 VL - 347 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.01.017/ DO - 10.1016/j.crma.2009.01.017 LA - en ID - CRMATH_2009__347_7-8_441_0 ER -
%0 Journal Article %A Ern, Alexandre %A Vohralík, Martin %T Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids %J Comptes Rendus. Mathématique %D 2009 %P 441-444 %V 347 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.01.017/ %R 10.1016/j.crma.2009.01.017 %G en %F CRMATH_2009__347_7-8_441_0
Ern, Alexandre; Vohralík, Martin. Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 441-444. doi : 10.1016/j.crma.2009.01.017. http://www.numdam.org/articles/10.1016/j.crma.2009.01.017/
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