On Some Aspects of the hp-FEM for Time-Harmonic Maxwell’s Equations

Abstract

Summary: It is well known that the design of suitable higher-order shape functions is essential for the performance of the $hp$-FEM. In this paper we propose a new family of hierarchic higher-order edge elements for the time-harmonic Maxwell's equations which are capable of reducing the condition number of the stiffness matrices dramatically compared to the currently best known hierarchic edge elements. The excellent conditioning properties of the new elements are illustrated by numerical examples.