A non-conforming composite quadrilateral finite element pair for feedback stabilization of the Stokes equations

P. Benner, J. Saak, F. Schieweck, P. Skrzypacz, H. K. Weichelt

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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 sub-triangles of each element.

Original languageEnglish
Pages (from-to)191-219
Number of pages29
JournalJournal of Numerical Mathematics
Volume22
Issue number3
DOIs
Publication statusPublished - Oct 1 2014

Keywords

  • Stokes equations
  • feedback stabilization
  • non-conforming finite elements

ASJC Scopus subject areas

  • Computational Mathematics

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