An Auto-Stabilized Weak Galerkin Method for Elasticity Interface Problems on Nonconvex Meshes

TL;DR

This paper presents an auto-stabilized weak Galerkin finite element method for elasticity interface problems on nonconvex meshes, eliminating the need for stabilizers and ensuring optimal error estimates.

Contribution

The paper introduces a novel auto-stabilized weak Galerkin method that simplifies implementation and improves stability for elasticity interface problems on general meshes.

Findings

Method is symmetric and positive definite.

Achieves optimal-order error estimates.

Numerical experiments confirm accuracy and efficiency.

Abstract

This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for elasticity interface problems on general polygonal and polyhedral meshes, without requiring convexity constraints. The method utilizes bubble functions as key analytical tools, eliminating the need for stabilizers typically used in traditional WG methods and leading to a more streamlined formulation. The proposed method is symmetric, positive definite, and easy to implement. Optimal-order error estimates are derived for the WG approximations in the discrete $H^1$-norm, assuming the exact solution has sufficient smoothness. Numerical experiments validate the accuracy and efficiency of the auto-stabilized WG method.