A posteriori analysis for a mixed FEM discretization of the linear elasticity spectral problem

TL;DR

This paper develops and analyzes reliable a posteriori error estimators for mixed finite element methods applied to the linear elasticity spectral problem, including nearly and perfectly compressible cases, supported by numerical tests.

Contribution

It introduces new a posteriori error estimators for mixed FEM discretizations of elasticity eigenvalue problems, with proofs of reliability and efficiency.

Findings

Estimators are reliable and efficient for elasticity spectral problems.

Numerical tests confirm theoretical results.

Method effectively handles nearly and perfectly compressible elasticity cases.

Abstract

In this paper we analyze a posteriori error estimates for a mixed formulation of the linear elasticity eigenvalue problem. A posteriori estimators for the nearly and perfectly compressible elasticity spectral problems are proposed. With a post-process argument, we are able to prove reliability and efficiency for the proposed estimators. The numerical method is based in Raviart-Thomas elements to approximate the pseudostress and piecewise polynomials for the displacement. We illustrate our results with numerical tests.