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 P(1) - P(0) (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
BEIRAO DA VEIGA, L., Lipnikov, K. (2010). A mimetic discretization of the stokes problem with selected edge bubbles. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 32(2), 875-893 [10.1137/090767029].
A mimetic discretization of the stokes problem with selected edge bubbles
BEIRAO DA VEIGA, LOURENCO;
2010
Abstract
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 P(1) - P(0) (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
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