Least-Squares Methods for Linear Elasticity: Refined Error Estimates

Abstract

We consider the linear elasticity problems and compare the approximations obtained by the Least-Squares finite element method with the approximations obtained by the standard conforming finite element method and the mixed finite element method. The main result is that the H1-conforming displacement approximations (least-squares finite element and standard finite element) as well as the H(div)-conforming stress approximations are higher-order pertubations of each other. This leads to refined a priori bounds and superconvergence results. Numerical experiments illustrate the theory.

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