A low-order locking-free multiscale finite element method for isotropic elasticity

TL;DR

This paper introduces a low-order, locking-free multiscale finite element method for isotropic elasticity that achieves optimal convergence and avoids Poisson locking, validated through numerical tests.

Contribution

It proposes a novel family of finite elements for elasticity that are multiscale, locking-free, and based on face degrees of freedom with local Neumann problems.

Findings

Method is well-posed with sufficient mesh refinement.

Achieves optimal convergence under local regularity.

Numerical tests confirm theoretical properties.

Abstract

The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a family of low-order finite elements for the linear elasticity problem which are free from Poisson locking. The finite elements rely on face degrees of freedom associated with multiscale bases obtained from local Neumann problems with piecewise polynomial interpolations on faces. We establish sufficient refinement levels on the fine-scale mesh such that the MHM method is well-posed, optimally convergent under local regularity conditions, and locking-free. Two-dimensional numerical tests assess theoretical results.