Curl-Conforming hierarchical vector bases for triangles and tetrahedra
Résumé
A new family of hierarchical vector bases is proposed for triangles and tetrahedra. These functions span the curl-conforming reduced-gradient spaces of N´ed´elec. The bases are constructed from orthogonal scalar polynomials to enhance their linear independence, which is a simpler process than an orthogonalization applied to the final vector functions. Specific functions are tabulated to order 6.5. Preliminary results confirm that the new bases produce reasonably well-conditioned matrices.