Abstract
In this paper, we analyze the error of a fictitious domain method with a Lagrange multiplier. It is applied to solve a non homogeneous elliptic Dirichlet problem with conforming finite elements of degree one on a regular grid. The main point is the proof of a uniform inf-sup condition that holds provided the step size of the mesh on the actual boundary is sufficiently large compared to the size of the interior grid.
Résumé
Dans cet article, nous étudions l’erreur d’une méthode de domaine fictif avec multiplicateur de Lagrange. Nous l’appliquons à la résolution d’un problème elliptique avec condition de Dirichlet non-homogène au bord par une méthode d’éléments finis conforme de degré un sur une grille uniforme. Ceci repose sur la démonstration d’une condition inf-sup uniforme qui est satisfaite lorsque le pas de la discrétisation sur la frontière du domaine d’origine est suffisamment grand comparé au pas de la grille intérieure.
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Girault, V., Glowinski, R. Error analysis of a fictitious domain method applied to a Dirichlet problem. Japan J. Indust. Appl. Math. 12, 487–514 (1995). https://doi.org/10.1007/BF03167240
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DOI: https://doi.org/10.1007/BF03167240