A Simple Weak Galerkin Finite Element Method for the Reissner-Mindlin Plate Model on Non-Convex Polytopal Meshes

TL;DR

This paper introduces a simple, stabilizer-free weak Galerkin finite element method for the Reissner-Mindlin plate model that works on complex non-convex polytopal meshes, offering flexibility and broad applicability.

Contribution

It develops a novel WG method that reduces stabilizer requirements, handles non-convex meshes, and allows flexible polynomial degrees, expanding the method's applicability.

Findings

Achieves optimal error estimates in discrete H^1 norm.

Validates theoretical results through numerical experiments.

Works effectively on non-convex polytopal meshes.

Abstract

This paper presents a simple weak Galerkin (WG) finite element method for the Reissner-Mindlin plate model that partially eliminates the need for traditionally employed stabilizers. The proposed approach accommodates general, including non-convex, polytopal meshes, thereby offering greater geometric flexibility. It utilizes bubble functions without imposing the restrictive conditions required by existing stabilizer-free WG methods, which simplifies implementation and broadens applicability to a wide range of partial differential equations (PDEs). Moreover, the method allows for flexible choices of polynomial degrees in the discretization and can be applied in any spatial dimension. We establish optimal-order error estimates for the WG approximation in a discrete H^1 norm, and present numerical experiments that validate the theoretical results.