A discrete elasticity complex on Alfeld splits

Abstract: We discuss what appears to be the first finite element elasticity sequence in 3d on tetrahedral meshes. We build this sequence using two discrete de Rham sequences that have more smoothness than the Whitney forms. To do this we use Alfeld splits that take a tetrahedral decomposition and split each tetrahedron into four tetrahedra by adding the barycenter. We provide degrees of freedom for the spaces as well as commuting projections. This is joint work with Snorre Christiansen, Kaibo Hu and Jay Gopalakrishnan.

numerical analysis

Audience: researchers in the topic

( paper )

Australian Seminar on Computational Mathematics

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