Analysis of a robust finite element approximation for a parabolic equation with rough boundary data

Abstract

The approximation of parabolic equations with nonhomogeneous Dirichlet boundary data by a numerical method that consists of finite elements for the space discretization and the backward Euler time discretization is studied. The boundary values are assumed in a least squares sense. It is shown that this method achieves an optimal rate of convergence for rough (only L 2 {L^2} ) boundary data and for smooth data as well. The results of numerical computations which confirm the robust theoretical error estimates are also presented.