Coupling DG-FEM and BEM for time harmonic eddy current problem

TL;DR

This paper presents a novel coupling of discontinuous Galerkin finite element methods with boundary element methods for solving time-harmonic eddy current problems, providing theoretical error bounds.

Contribution

It introduces a new DG-FEM/BEM coupling approach for magnetic field problems and proves quasi-optimal error estimates in the energy norm.

Findings

Proves quasi-optimal error estimates for the coupled method

Demonstrates the effectiveness of nonconforming Nédélec elements in this context

Provides a rigorous mathematical analysis of the coupling technique

Abstract

We introduce and analyze a discontinuous Galerkin FEM/BEM method for a time-harmonic eddy current problem written in terms of the magnetic field. We use nonconforming N\'ed\'elec finite elements on a partition of the interior domain coupled with continuous boundary elements on the transmission interface. We prove quasi-optimal error estimates in the energy norm.