Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 418
Two-dimensional extension of a penalization method for Neumann or Robin boundary conditions
Bouchra Bensiali, Jacques Liandrat
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 31, 2022
March 03, 2352
April 15, 2352

Abstract: In a previous paper, a fictitious domain penalization method to take account of Neumann or Robin boundary conditions has been proposed and analyzed mostly in one dimensional space. Here, we present a n-dimensional extension of this method. The existence and uniqueness of the solution of the penalized problem are obtained using the approach of Droniou for non-coercive linear elliptic problems. The convergence of the penalization method with respect to the penalization parameter η is investigated numerically in two dimensions using adequate finite differences or finite elements suitable for ...