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A new family of hierarchical vector bases is proposed for triangles and tetrahedra. These functions span the curl-conforming reduced-gradient spaces of Nédélec. 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.
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Graglia et al. (2011) studied this question.
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