A Weak Galerkin Least-squares Finite Element Method for Div-curl Systems

Jichun Li, University of Nevada, Las Vegas
Xiu Ye, University of Arkansas at Little Rock
Shangyou Zhang, University of Delaware


In this paper, we introduce a weak Galerkin least-squares method for solving div–curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.