A discontinuous Galerkin method for the time harmonic eddy current problem
This work provides a rigorous numerical analysis for a specific computational electromagnetics problem, but is incremental as it extends existing DG techniques to a coupled formulation.
The authors propose and analyze a discontinuous Galerkin method for the time-harmonic eddy current problem, achieving uniform stability and quasi-optimal error estimates in the DG-energy norm.
We introduce and analyze a discontinuous Galerkin method for a time-harmonic eddy current problem formulated in terms of the magnetic field. The scheme is obtained by putting together a DG method for the approximation of the vector field variable representing the magnetic field in the conductor and a DG method for the Laplace equation whose solution is a scalar magnetic potential in the insulator. The transmission conditions linking the two problems are taken into account weakly in the global discontinuous Galerkin scheme. We prove that the numerical method is uniformly stable and obtain quasi-optimal error estimates in the DG-energy norm.