Higher-order compatible discretization on hexahedrals
Mathematical Physics
2013-04-29 v1 Computational Engineering, Finance, and Science
Computational Geometry
Numerical Analysis
math.MP
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.
Cite
@article{arxiv.1304.7018,
title = {Higher-order compatible discretization on hexahedrals},
author = {Jasper Kreeft and Marc Gerritsma},
journal= {arXiv preprint arXiv:1304.7018},
year = {2013}
}
Comments
to appear in Lecture Notes in Computational Science and Engineering