A penalized Robin approach for solving a parabolic equation with nonsmooth Dirichlet boundary conditions

Article type: Research Article

Authors: Ben Belgacem, F. | El Fekih, H. | Raymond, J.P.

Affiliations: Mathématiques pour l'Industrie et la Physique, UMR 5640, Université Paul Sabatier, 31062 Toulouse cedex 04, France E‐mail: belgacem@mip.ups‐tlse.fr, raymond@mip.ups‐tlse.fr | École Nationale d'Ingénieurs de Tunis, LAMSIN, BP 37, 1002 Tunis‐Belvédère, Tunisie E‐mail: henda.elfekih@enit.rnu.tn

Abstract: We study the approximation of a parabolic equation with a nonsmooth Dirichlet boundary condition by equations with Robin boundary conditions. We give the convergence rate, in some suitable anisotropic Sobolev spaces, of the penalized solution towards the Dirichlet solution when the penalty parameter ε>0 becomes small. Some numerical tests, presented at the end of the paper, illustrate the theoretical estimates.

Keywords: parabolic equations, singular perturbation, dual variational formulation, anisotropic Sobolev spaces, nonsmooth Dirichlet boundary condition

Journal: Asymptotic Analysis, vol. 34, no. 2, pp. 121-136, 2003