Singular Hierarchical Curl-Conforming Vector Bases for Triangular Cells

A new family of hierarchical vector basis functions is proposed that accurately models fields near corners. These are additive functions that combine singular bases incorporating general exponents with a full set of existing hierarchical polynomial basis functions to form the representation. The functions are described for triangular cells, and several results are provided to illustrate the improvement in accuracy resulting from their use. A simple method for numerically constructing the singular basis functions “on the fly” is also provided. The numerical construction of these singular basis functions facilitates their use for modeling fields near corners made of penetrable material.