An error estimate for finite element approximation to elliptic PDEs with discontinuous Dirichlet boundary data

Abstract

This note provides an error estimate for finite element approximation to elliptic partial differential equations (PDEs) with discontinuous Dirichlet boundary data. Solutions of problems of this type are not in H1 and, hence, the standard variational formulation is not valid. To circumvent this difficulty, an error estimate of a finite element approximation in the W1,r(Ω) (0<r<2) norm is obtained through a regularization by constructing a continuous approximation of the Dirichlet boundary data.