A simple pressure stabilization method for the Stokes equation

In this paper, we consider a stabilization method for the Stokes problem, using equal‐order interpolation of the pressure and velocity, which avoids the use of the mesh size parameter in the stabilization term. We show that our approach is stable for equal‐order interpolation in the case of piecewis...

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Vydáno v:Communications in numerical methods in engineering Ročník 24; číslo 11; s. 1421 - 1430
Hlavní autoři: Becker, Roland, Hansbo, Peter
Médium: Journal Article
Jazyk:angličtina
Vydáno: Chichester, UK John Wiley & Sons, Ltd 01.11.2008
Wiley
Témata:
Beräkningsmatematik
Computational Mathematics
Computational techniques
equal-order interpolation
Exact sciences and technology
Fluid dynamics
Fluid Mechanics
Fundamental areas of phenomenology (including applications)
General theory
Mathematical methods in physics
Physics
stabilization
Stokes problem
Strömningsmekanik
Incompressible flow
Stokes problem
Stokes equation
Stabilization
Polynomial approximation
Quadratic approximation
equal-order interpolation
Piecewise linear system
ISSN:1069-8299, 1099-0887, 1099-0887
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Shrnutí:In this paper, we consider a stabilization method for the Stokes problem, using equal‐order interpolation of the pressure and velocity, which avoids the use of the mesh size parameter in the stabilization term. We show that our approach is stable for equal‐order interpolation in the case of piecewise linear and piecewise quadratic polynomials on triangles. In the case of linear polynomials, we retrieve a well‐known idea of using mass lumping as a stabilization mechanism. Copyright © 2007 John Wiley & Sons, Ltd.
Bibliografie:ArticleID:CNM1041
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content type line 23
ISSN:1069-8299
1099-0887
1099-0887
DOI:10.1002/cnm.1041