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

journal contribution
posted on 2023-06-07, 20:26 authored by Erik Burman, Miguel A Fernández
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.

History

Publication status

  • Published

Journal

SIAM Journal on Numerical Analysis

ISSN

0036-1429

Publisher

Society for Industrial and Applied Mathematics

Issue

1

Volume

47

Page range

409-439

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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