A locking-free discontinuous Galerkin method for linear elastic Steklov eigenvalue problem

TL;DR

This paper introduces a locking-free discontinuous Galerkin method for solving the Steklov eigenvalue problem in linear elasticity, providing error estimates and demonstrating robustness through numerical experiments.

Contribution

The paper develops a novel Nitsche's discontinuous Galerkin method that is locking-free and effective for nearly incompressible materials in linear elasticity eigenvalue problems.

Findings

The method achieves optimal error estimates under low regularity.

It is robust for nearly incompressible materials.

Numerical experiments confirm effectiveness and robustness.

Abstract

In this paper, a discontinuous Galerkin finite element method of Nitsche's version for the Steklov eigenvalue problem in linear elasticity is presented. The a priori error estimates are analyzed under a low regularity condition, and the robustness with respect to nearly incompressible materials (locking-free) is proven. Furthermore, some numerical experiments are reported to show the effectiveness and robustness of the proposed method.