A Two-Dimensional Self-Adaptive hp Finite Element Method for the Analysis of Open Region Problems in Electromagnetics

A two-dimensional self-adaptive hp finite element method (FEM) for the analysis of open region problems in electromagnetics is presented. An iterative FEM methodology for open region problems proposed by the authors is used. It reduces the solution of the open region problem to the solution of a low number of closed domain problems with very low computational cost for the second and subsequent iterations. Thus, the particularities due to the open nature of the problem are hidden and, among other advantages, self-adaptive strategies developed for conventional closed domains and, specifically, of hp type, can be used without modifications. The hp-FEM discretization is made in terms of quadrangles/triangles of variable order of approximation supporting anisotropy and hanging nodes. The adaptive strategy is fully automatic and is based on minimizing the interpolation error (by using the projection of the error from a fine grid) delivering exponential convergence rates for the energy error, even in the presence of singularities