Many commonly used mixed finite elements for the Stokes problem only conserve mass approximately. We show that if we supplement polynomial basis functions with divergence free rational functions in the finite element method we can conserve mass exactly. Similarly, we show how to supplement polynomial basis in the finite element space with rational functions in when approximating linear elasticity problems in order to preserve angular momentum exactly. This is joint work with Michael Neilan (University of Pittsburgh).

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Last updated: 24 Mar 2023