Analysis of a Robust Finite Element Approximation for a Parabolic Equation with Rough Boundary Data

Abstract

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 L1) boundary data and for smooth data as well. The results of numerical computations which confirm the robust theoretical error estimates are also presented.

Numerical Analysis and Computation of Nonlinear Partial Differential Equations from Applied Mathematics

“…In this research finite element methods were applied to a simple model of shear band formation in [FG] and [ARO2]. They were also used for elliptic and parabolic problems that arise in optimal control in [FK1] and [FK2] and for equations that simulate phase transitions in [FJ1] and [ARO1]. These finite element schemes were analyzed and implemented.…”