In this paper, we derive new two-sided a posteriori estimates of the modeling errors for linear elliptic boundary value problems with periodic coefficients solved by homogenization. Our approach is based on the concept of functional a posteriori error estimation. The estimates are obtained for the energy norm and use solely the global flux of the non-oscillatory solution of the homogenized model and solution of a boundary value problem on the cell of periodicity.
Dans cette Note, nous obtenons de nouvelles estimations de lʼerreur de modélisation pour des problèmes elliptiques linéaires dʼhomogénéisation à coefficients périodiques. Notre approche est fondée sur le concept dʼestimation a posteriori fonctionnelle. Nos estimations sont obtenues pour la norme dʼénergie et utilisent seulement le flux de la solution non oscillante du problème homogénéisé et la solution dʼun problème aux limites sur la cellule de périodicité.
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Sergey I. Repin 1; Tatiana S. Samrowski 2; Stefan A. Sauter 3
@article{CRMATH_2013__351_23-24_877_0, author = {Sergey I. Repin and Tatiana S. Samrowski and Stefan A. Sauter}, title = {A posteriori error majorants of the modeling errors for elliptic homogenization problems}, journal = {Comptes Rendus. Math\'ematique}, pages = {877--882}, publisher = {Elsevier}, volume = {351}, number = {23-24}, year = {2013}, doi = {10.1016/j.crma.2013.10.025}, language = {en}, }
TY - JOUR AU - Sergey I. Repin AU - Tatiana S. Samrowski AU - Stefan A. Sauter TI - A posteriori error majorants of the modeling errors for elliptic homogenization problems JO - Comptes Rendus. Mathématique PY - 2013 SP - 877 EP - 882 VL - 351 IS - 23-24 PB - Elsevier DO - 10.1016/j.crma.2013.10.025 LA - en ID - CRMATH_2013__351_23-24_877_0 ER -
%0 Journal Article %A Sergey I. Repin %A Tatiana S. Samrowski %A Stefan A. Sauter %T A posteriori error majorants of the modeling errors for elliptic homogenization problems %J Comptes Rendus. Mathématique %D 2013 %P 877-882 %V 351 %N 23-24 %I Elsevier %R 10.1016/j.crma.2013.10.025 %G en %F CRMATH_2013__351_23-24_877_0
Sergey I. Repin; Tatiana S. Samrowski; Stefan A. Sauter. A posteriori error majorants of the modeling errors for elliptic homogenization problems. Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 877-882. doi : 10.1016/j.crma.2013.10.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.025/
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