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

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.