A modified weak Galerkin method for $\boldsymbol{H}(\mathrm{curl})$-elliptic problem

TL;DR

This paper introduces a modified weak Galerkin finite element method for solving $oldsymbol{H}( ext{curl})$-elliptic problems, featuring a new discrete curl operator and optimal error estimates without penalty parameters.

Contribution

The paper develops a novel MWG method with a new discrete curl operator that avoids penalty parameters, improving stability and accuracy for $oldsymbol{H}( ext{curl})$ problems.

Findings

Proves optimal error estimates in energy norm.

Demonstrates the method's effectiveness through numerical results.

Eliminates the need for penalty parameters in the MWG method.

Abstract

In this paper, we design and analysis a modified weak Galerkin (MWG) finite element method for $\boldsymbol{H}(\mathrm{curl})-$elliptic problem. We first introduce a new discrete weak curl operator and the MWG finite element space. The modified weak Galerkin method does not require the penalty parameter by comparing with traditional DG methods. We prove optimal error estimates in energy norm. At last, we provide the numerical results to confirm these theoretical results.