Singular, Hierarchical Scalar Basis Functions for Triangular Cells

A new family of hierarchical basis functions is proposed for triangular cells. These functions incorporate singular behavior to model fields with corner singularities. The functions are of the additive kind, and combine a traditional polynomial-complete representation on triangles with additional singular terms that incorporate general exponents that may be adjusted for the specific wedge angle of interest. The condition numbers arising from the use of these functions is investigated.