In this Note we deal with the finite element approximation of a transmission problem across a prefractal curve approximating the von Koch fractal curve. We construct a mesh adapted to the geometric shape of the interface and we refine it consistently with some estimates in suitable weighted Sobolev spaces. In these spaces we also obtain an approximation error estimate.
Cette Note concerne l'approximation éléments finis d'un problème de transmission à travers la courbe préfractale approchant la courbe fractale de von Koch. On construit un maillage adapté à la géométrie de l'interface et on génère un processus de raffinement de maillage en utilisant des estimations dans des espaces de Sobolev à poids, choisis convenablement. On obtient aussi dans ces espaces une estimation de l'erreur d'approximation.
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@article{CRMATH_2006__342_3_211_0, author = {Bagnerini, Patrizia and Buffa, Annalisa and Vacca, Elisa}, title = {Finite elements for a prefractal transmission problem}, journal = {Comptes Rendus. Math\'ematique}, pages = {211--214}, publisher = {Elsevier}, volume = {342}, number = {3}, year = {2006}, doi = {10.1016/j.crma.2005.11.023}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.11.023/} }
TY - JOUR AU - Bagnerini, Patrizia AU - Buffa, Annalisa AU - Vacca, Elisa TI - Finite elements for a prefractal transmission problem JO - Comptes Rendus. Mathématique PY - 2006 SP - 211 EP - 214 VL - 342 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.11.023/ DO - 10.1016/j.crma.2005.11.023 LA - en ID - CRMATH_2006__342_3_211_0 ER -
%0 Journal Article %A Bagnerini, Patrizia %A Buffa, Annalisa %A Vacca, Elisa %T Finite elements for a prefractal transmission problem %J Comptes Rendus. Mathématique %D 2006 %P 211-214 %V 342 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.11.023/ %R 10.1016/j.crma.2005.11.023 %G en %F CRMATH_2006__342_3_211_0
Bagnerini, Patrizia; Buffa, Annalisa; Vacca, Elisa. Finite elements for a prefractal transmission problem. Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 211-214. doi : 10.1016/j.crma.2005.11.023. http://archive.numdam.org/articles/10.1016/j.crma.2005.11.023/
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