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Stabilized finite element methods based on multiscale enrichment for the Stokes problem

Araya, R. and Barrenechea, G.R. and Valentin, F. (2006) Stabilized finite element methods based on multiscale enrichment for the Stokes problem. SIAM Journal on Numerical Analysis, 44 (1). ISSN 0036-1429

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Abstract

This work concerns the development of stabilized finite element methods for the Stokes problem considering nonstable different (or equal) order of velocity and pressure interpolations. The approach is based on the enrichment of the standard polynomial space for the velocity component with multiscale functions which no longer vanish on the element boundary. On the other hand, since the test function space is enriched with bubble-like functions, a Petrov--Galerkin approach is employed. We use such a strategy to propose stable variational formulations for continuous piecewise linear in velocity and pressure and for piecewise linear/piecewise constant interpolation pairs. Optimal order convergence results are derived and numerical tests validate the proposed methods.

Item type: Article
ID code: 4883
Keywords: Stokes equation, multiscale functions, SIMPLEST element, bubble function, numerical analysis, Mathematics
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Strathprints Administrator
    Date Deposited: 27 Nov 2007
    Last modified: 12 Mar 2012 10:41
    URI: http://strathprints.strath.ac.uk/id/eprint/4883

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