A weak Galerkin finite element method for indefinite time-harmonic Maxwell equations

Abstract

In this paper, we intend to develop a weak Galerkin (WG) finite element method for solving the indefinite time-harmonic Maxwell equations. Firstly, by using an analogy of Ga˚rding inequality and proving a posteriori estimate about the error, we prove the well-posedness of the WG method. Then, by deducing an error equation, we achieve optimal a priori error estimates in both the energy norm and the L2 norm. Finally, we carry out some numerical experiments to confirm the theoretical conclusions.