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 journalArticle

2 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
Externally publishedYes

Fingerprint

Feedback Stabilization
Stokes Equations
Stabilization
Composite
Finite Element
Feedback
Mathematical operators
Composite materials
Boundary Stabilization
Mass Conservation
Stokes Problem
Hermann Von Helmholtz
Galerkin methods
Operator Equation
Condensation
Sparsity
Galerkin Method
Notation
Partial differential equations
Basis Functions

Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics

Cite this

A non-conforming composite quadrilateral finite element pair for feedback stabilization of the Stokes equations. / Benner, P.; Saak, J.; Schieweck, F.; Skrzypacz, P.; Weichelt, H. K.

In: Journal of Numerical Mathematics, Vol. 22, No. 3, 01.10.2014, p. 191-219.

Research output: Contribution to journalArticle

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