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1 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres 2 I2M - Institut de Mathématiques de Marseille

Abstract : This paper is devoted to the mathematical analysis of a method based on fictitious domain approach. Boundary conditions of Robin type also known as Fourier boundary conditions are enforced using a penalization method. A complete description of the method and a full analysis are provided for univariate elliptic and parabolic problems using finite difference approximation. Numerical evidence of the predicted estimations is provided as well as numerical results for a nonlinear problem and a first extension of the method in the bivariate situation is proposed.

Keywords : 65M06 65N85 fictitious domain methods penalization Robin boundary conditions finite difference methods 2010 MSC: Primary 65M85 65N06

Author: Bouchra Bensiali - Guillaume Chiavassa - Jacques Liandrat -



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