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Exact smooth piecewise polynomial sequences on Alfeld splits Neilan, Michael


We develop exact polynomial sequences on Alfeld splits in any spatial dimension and for any polynomial degree. An Alfeld split of a tetrahedron is obtained by connecting the vertices of an $n$-simplex with its barycenter. We show that, on these triangulations, the kernel of the exterior derivative has enhanced smoothness. Byproducts of this theory include characterizations of discrete divergence-free subspaces for the Stokes problem, commutative projections, and simple formulas for the dimensions of smooth polynomial spaces. This is joint work with Guosheng Fu and Johnny Guzmán.

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