A Computational Study of the Weak Galerkin Method for Second-Order Elliptic Equations

TL;DR

This paper computationally investigates the weak Galerkin finite element method for second-order elliptic equations on diverse meshes, confirming its efficiency, robustness, and reliability through numerical results.

Contribution

It extends the analysis of the weak Galerkin method to more general partitions and validates its effectiveness across various model problems.

Findings

Numerical results confirm the theoretical properties.

The method is efficient and robust.

It performs reliably on diverse mesh types.

Abstract

The weak Galerkin finite element method is a novel numerical method that was first proposed and analyzed by Wang and Ye for general second order elliptic problems on triangular meshes. The goal of this paper is to conduct a computational investigation for the weak Galerkin method for various model problems with more general finite element partitions. The numerical results confirm the theory established by Wang and Ye. The results also indicate that the weak Galerkin method is efficient, robust, and reliable in scientific computing.