Local multiscale model reduction using discontinuous Galerkin coupling for elasticity problems

TL;DR

This paper develops a discontinuous Galerkin coupled multiscale finite element method for linear elasticity in heterogeneous media, providing convergence proof and demonstrating its advantages through numerical examples.

Contribution

It introduces a novel DG version of the CEM-GMsFEM for elasticity, including auxiliary and offline basis functions, with a first-time convergence proof.

Findings

Method achieves accurate multiscale elasticity solutions

Provides flexibility in coarse grid construction

Demonstrates convergence and efficiency in numerical tests

Abstract

In this paper, we consider the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with discontinuous Galerkin (DG) coupling for the linear elasticity equations in highly heterogeneous and high contrast media. We will introduce the construction of a DG version of the CEM-GMsFEM, such as auxiliary basis functions and offline basis functions. The DG version of the method offers some advantages such as flexibility in coarse grid construction and sparsity of resulting discrete systems. Moreover, to our best knowledge, this is the first time where the proof of the convergence of the CEM-GMsFEM in the DG form is given. Some numerical examples will be presented to illustrate the performance of the method.