1. Higher-order compatible discretization on hexahedrals
- Author
-
Kreeft, Jasper and Gerritsma, Marc
- Subjects
Computational Engineering, Finance, and Science (cs.CE) ,Computational Geometry (cs.CG) ,FOS: Computer and information sciences ,FOS: Mathematics ,Computer Science - Numerical Analysis ,FOS: Physical sciences ,Computer Science - Computational Geometry ,Mathematical Physics (math-ph) ,Numerical Analysis (math.NA) ,Computer Science - Computational Engineering, Finance, and Science ,Mathematical Physics - 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., to appear in Lecture Notes in Computational Science and Engineering
- Published
- 2013