Decoupled weak Galerkin finite element method for Maxwell’s equations

We consider Maxwell’s equations in a decoupled formulation by introducing Lagrange multipliers and obtain the magnetic field given the known electric field. The proposed formulation combines the decoupled weak form with the four equations of Maxwell’s model. The decoupled system reduces the computational complexity by restricting the degrees of freedom of the electric or magnetic fields. We present the construction of mixed weak Galerkin finite element methods for electric field and magnetic field, utilizing backward Euler time discretization in fully discrete schemes. We analyze the error estimate of the electric and magnetic field in the energy norm. Finally, we present numerical results for the proposed schemes in three-dimensional space to validate our theory.