A Weak Galerkin Finite Element Method for a $H({\rm curl})$-Elliptic Problem

Abstract

In this paper, we develop and analyze a weak Galerkin (WG) finite element method for solving a $H({\rm curl})$-elliptic problem. With the aid of the weak curl operator and a stabilizer term, we first design a WG discretization. Then, by using an auxiliary problem and establishing an error equation, we achieve the optimal order error estimates in both the energy norm and $L^2$ norm for the WG method. At last, we report some numerical experiments to confirm the theoretical results.