On the convergence and stability of the standard least squares finite element method for first-order elliptic systems

Abstract

A general framework of the theoretical analysis for the convergence and stability of the standard least squares finite element approximations to boundary value problems of first-order linear elliptic systems is established in a natural norm. With a suitable density assumption, the standard least squares method is proved to be convergent without requiring extra smoothness of the exact solutions. The method is also shown to be stable with respect to the natural norm. Some representative problems such as the grad-div type problems and the Stokes problem are demonstrated. (C) 1998 Published by Elsevier Science Inc. All rights reserved.