Energy norm analysis of exactly symmetric mixed finite elements for linear elasticity

TL;DR

This paper develops new error estimates for symmetric mixed finite element methods in linear elasticity, ensuring accuracy across different material compressibility levels, validated by numerical tests.

Contribution

It introduces a quasi-optimal a priori error estimate and a novel a posteriori estimate valid in the incompressible limit for symmetric mixed finite elements.

Findings

Error estimates are uniform with respect to compressibility.

Numerical examples confirm theoretical results.

New a posteriori estimate enhances adaptive methods.

Abstract

We consider mixed finite element methods with exact symmetric stress tensors. We derive a new quasi-optimal a priori error estimate uniformly valid with respect to the compressibility. For the a posteriori error analysis we consider the Prager-Synge hypercircle principle and introduce a new estimate uniformly valid in the incompressible limit. All estimates are validated by numerical examples.