A Well-Conditioned Hierarchical Basis for Triangular H(curl)-Conforming Elements (Communications in Computational Physics, 2011)
We construct a well-conditioned hierarchical basis for triangular H(curl)-conforming elements with selected orthogonality. The basis functions are grouped intoedge and interior functions, and the later is further grouped into normal and bubblefunctions. In our construction, the trace of the edge shape functions are orthonormalon the associated edge. The interior normal functions, which are perpendicular toan edge, and the bubble functions are both orthonormal among themselves over thereference element. The construction is made possible with classic orthogonal polynomials,viz., Legendre and Jacobi polynomials. For both the mass matrix and thequasi-stiffness matrix, better conditioning of the new basis is shown by a comparisonwith the basis previously proposed by Ainsworth and Coyle [Comput. Methods.Appl. Mech. Engrg., 190 (2001), 6709-6733].