Discretization errors in finite methods: issues and possible solutions Original Research Article

In this paper, we review many of the sources of discretization error when finite methods is applied to high frequency electromagnetic problems. A major source of error is the numerical dispersion error. This error is probably the most serious error for electrically large geometries, and we review past efforts to reduce this error. We also present a new edge-based finite difference method which offers several improvements to current finite difference. This new method has less numerical dispersion error and less errors due to material discontinuities than current finite difference methods. We compare its performance to vector finite elements and show its superior accuracy. Finally, we propose a new subgridding scheme to reduce discretization error which maintains second-order accuracy.