Hierarchical and singular bases for finite methods

Abstract

Hierarchical basis function families that incorporate singular behavior to model fields with corner singularities are reviewed. These families are of the additive kind, and combine a traditional polynomial-complete representation with additional singular terms that incorporate general exponents that may be adjusted for the specific wedge angle of interest. A few results are reported to validate the benefits of using such bases when dealing with two-dimensional structures with corners meshed with triangular cells.