Displacement-pseudostress formulation for the linear elasticity spectral problem

TL;DR

This paper introduces a mixed finite element approach for the elasticity spectral problem, ensuring convergence and avoiding spurious modes, with theoretical analysis and numerical validation.

Contribution

It proposes a novel displacement-pseudostress formulation using Raviart-Thomas elements, with proven convergence and error estimates for the elasticity eigenvalue problem.

Findings

Method converges without spurious modes

Error estimates are established

Numerical tests support theoretical results

Abstract

In this paper we analyze a mixed displacement-pseudostress formulation for the elasticity eigenvalue problem. We propose a finite element method to approximate the pseudostress tensor with Raviart-Thomas elements and the displacement with piecewise polynomials. With the aid of the classic theory for compact operators, we prove that our method is convergent and does not introduce spurious modes. Also, we obtain error estimates for the proposed method. Finally, we report some numerical tests supporting the theoretical results.