A non-conforming composite quadrilateral finite element pair for feedback stabilization of the stokes equations / Peter Benner, Jens Saak, Friedhelm Schieweck, Piotr Skrzypacz, Heiko K. Weichelt
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A non-conforming composite quadrilateral finite element pair for feedback stabilization of the stokes equations
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870364111
URN
urn:nbn:de:gbv:3:2-64101
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Publication history
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, October 19, 2012
Content
1 Online-Ressource (25 Seiten = 0,83 MB) : Diagramme
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Language
eng
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Abstract
Abstract: In this contribution, we show a method for the boundary feedback stabilization of the Stokes problem around a stationary trajectory. We derive a formal low-rank algorithm for solving the stabilization problem in operator notation. The appearing operator equations are formulated in terms of stationary partial differential equations (PDEs) instead of using their finite dimensional representations in terms of matrices. A Galerkin method, satisfying the divergence constraint pointwise locally is especially appealing since it represents appropriately the action of the Helmholtz projection. The main advantages of the composite technique are the efficient assembly of element matrices, the reduction of computational costs using static condensation, and the diagonal mass matrix. The non-conforming character of the composite element guarantees a better sparsity pattern, compared to conforming elements, due to the lower number of couplings between basis functions corresponding to neighboring cells. We also achieve the pointwise mass conservation on subtriangles of each element.
Series
Max Planck Institute Magdeburg Preprints ; 12-19 ppn:870173030