p-Refinement Techniques for Vector Finite Elements in Electromagnetics

Abstract

The vector finite element method has gained great attention since overcoming the deficiencies incurred by the scalar basis functions for the vector Helmholtz equation. Most implementations of vector FEM have been non-adaptive, where a mesh of the domain is generated entirely in advance and used with a constant degree polynomial basis to assign the degrees of freedom. To reduce the dependency on the users' expertise in analyzing problems with complicated boundary structures and material characteristics, and to speed up the FEM tool, the demand for adaptive FEM grows high.

For efficient adaptive FEM, error estimators play an important role in assigning additional degrees of freedom. In this proposal study, hierarchical vector basis functions and four error estimators for p-refinement are investigated for electromagnetic applications.