Mathematics – Numerical Analysis
Scientific paper
2012-01-20
Mathematics
Numerical Analysis
Scientific paper
In this paper we apply the recently developed mimetic discretization method [44] to the mixed formulation of the Stokes problem in terms of the vorticity-velocity-pressure formulation. The mimetic discretization presented in this paper and in [44] is a higher-order method for curvilinear quadrilaterals. It relies on the language of differential $k$-forms, $k$-cochains as its discrete counterpart, and the relations between them in terms of the mimetic operators: reduction, reconstruction and projection. The reconstruction consists of a mimetic spectral element method. The most important result of the mimetic framework is the commutation between differentiation at the continuous level with that on the finite dimensional and discrete level. As a result operators like gradient, curl and divergence are discretized exactly. For Stokes flow, this implies a pointwise divergence-free solution. This is confirmed using a set of test cases on both Cartesian and curvilinear meshes. It will be shown that the method preforms optimally for all admissible boundary conditions.
Gerritsma Marc
Kreeft Jasper
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