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High-Order Divergence-Conforming Constrained Bases for Triangular Cells

This paper presents an algebraic technique for generating arbitrary-order divergence-conforming bases for curvilinear triangular cells. The bases are constructed by enforcing appropriate constraints on a linear combination of general functions and then extracting the desired bases using singular value decompositions. Koornwinder–Dubiner polynomials are chosen as the general function set. Basic constraints are presented to obtain divergence-conforming bases, and additional constraints are presented to further enforce the bases to be Nédélec. Results from a variety of problems are given to show that the bases exhibit high-order convergence and also produce systems that are relatively well conditioned compared to other basis sets.