A Primal-Dual Weak Galerkin Method for Div-Curl Systems with low-regularity solutions

Abstract

This article presents a new primal-dual weak Galerkin finite element method for the div-curl system with tangential boundary conditions and low-regularity assumptions on the solution. The numerical scheme is based on a weak variational form involving no partial derivatives of the exact solution supplemented by a dual or ajoint problem in the general context of the weak Galerkin finite element method. Optimal order error estimates in $L^2$ are established for solution vector fields in $H^{\theta }(\Omega ),\theta >\frac{1}{2}$. The mathematical theory was derived on connected domains with general topological properties (namely, arbitrary first and second Betti numbers). Numerical results are reported to confirm the theoretical convergence.

References in corpus (2)

• A primal-dual finite element method for first-order transport problems
• A Primal-Dual Weak Galerkin Finite Element Method for Fokker-Planck Type Equations