Evaluation of Hierarchical Vector Basis Functions for Quadrilateral Cells

New hierarchical vector basis functions for quadrilateral cells are introduced, and the matrix condition numbers associated with their use are compared to those of existing vector basis families to assess the relative linear independence of the functions. Scale factors are employed to improve the condition numbers. In addition, the proper use of subsets of these families to transition from one order to another (as needed for adaptive p-refinement) without exciting spurious modes is considered.