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arXiv · 1304.7018

Higher-order compatible discretization on hexahedrals

Jasper Kreeft·Marc Gerritsma
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Abstract

We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constructed. As a sample problem we consider the vorticity-velocity-pressure formulation of the Stokes problem. We motivate the choice for a mixed variational formulation based on both geometric as well as physical arguments. Numerical tests confirm the theoretical results that we obtain a pointwise divergence-free solution for the Stokes problem and that the method obtains optimal convergence rates.

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Jasper Kreeft, Marc Gerritsma. 2013-04-25. Higher-order compatible discretization on hexahedrals. https://arxiv.org/abs/1304.7018

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