Galerkin finite element methods with symmetric pressure stabilization for the transient stokes equations: Stability and convergence analysis

Burman, Erik and Fernández, Miguel A (2008) Galerkin finite element methods with symmetric pressure stabilization for the transient stokes equations: Stability and convergence analysis. SIAM Journal on Numerical Analysis, 47 (1). pp. 409-439. ISSN 0036-1429

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Abstract

We consider the stability and convergence analysis of pressure stabilized finite element approximations of the transient Stokes equation. The analysis is valid for a class of symmetric pressure stabilization operators, but also for standard, inf-sup stable, velocity/pressure spaces without stabilization. Provided the initial data are chosen as a specific (method-dependent) Ritz-projection, we get unconditional stability and optimal convergence for both pressure and velocity approximations, in natural norms. For arbitrary interpolations of the initial data, a condition between the space and time discretization parameters has to be verified in order to guarantee pressure stability.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 18:32
Last Modified: 20 Jun 2012 14:22
URI: http://sro.sussex.ac.uk/id/eprint/17003
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