A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles
A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The mimetic discretization methodology can be understood as a generalization of the finite element method to meshes with general polygons/polyhedrons. In this paper, the mimetic generalization of the unstable P1...
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| Veröffentlicht in: | SIAM journal on scientific computing 2010-01, Vol.32 (2), p.875-893 |
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| creator | da Veiga, L. Beirão Lipnikov, K. |
| description | A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The mimetic discretization methodology can be understood as a generalization of the finite element method to meshes with general polygons/polyhedrons. In this paper, the mimetic generalization of the unstable P1 - P0 (and the "conditionally stable" Q1 - P0) finite element is shown to be fully stable when applied to a large range of polygonal meshes. Moreover, we show how to stabilize the remaining cases by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1137/090767029 |
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| subjects | Bubbles Combinatorics Discretization Finite difference method Finite element analysis Finite element method Fluid flow Mathematical analysis Numerical analysis Polygons Polyhedra Polyhedrons Strategy Studies |
| title | A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles |
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