Interior Penalty Discontinuous Galerkin Method for Magnetostatic Field Problems in Two Dimensions

An interior penalty discontinuous Galerkin method for solving 2-D magnetostatic field problems using the magnetic vector potential ${A}$ is presented. The use of the ${A}$ -formulation in two dimensions results in a second-order elliptic boundary value problem. Due to the proposed method, the scheme is symmetric and the resulting mass matrix is block diagonal, whereas each block belongs to one element of the triangulation. The applicability of the method is demonstrated by solving a simple 2-D C-shaped ferromagnetic material with a coil surrounding one part of the magnetic yoke. Thereby, the permeability of the material is supposed to be homogeneous and isotropic. The solution ${A}$ and the resulting field quantities are compared with the standard finite element analysis.