Burman, E;
Fernandez, MA;
(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.
10.1137/070707403.
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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.
| Type: | Article |
|---|---|
| Title: | Galerkin Finite Element Methods with Symmetric Pressure Stabilization for the Transient Stokes Equations: Stability and Convergence Analysis |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/070707403 |
| Publisher version: | http://dx.doi.org/10.1137/070707403 |
| Language: | English |
| Additional information: | Copyright © 2008 Society for Industrial and Applied Mathematics |
| Keywords: | transient Stokes equations, finite element methods, symmetric pressure stabilization, time discretization, Ritz-projection |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1384740 |
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