Galerkin finite element methods with symmetric pressure stabilization for the transient Stokes' equations: stability and convergence analysis - Archive ouverte HAL Access content directly
Journal Articles SIAM Journal on Numerical Analysis Year : 2008

Galerkin finite element methods with symmetric pressure stabilization for the transient Stokes' equations: stability and convergence analysis

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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. Provided the initial data is chosen as a specific (pressure stabilization 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 guarantee pressure stability
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Dates and versions

inria-00178359 , version 1 (10-10-2007)
inria-00178359 , version 2 (11-10-2007)
inria-00178359 , version 3 (24-06-2008)

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Erik Burman, Miguel Angel Fernández. Galerkin finite element methods with symmetric pressure stabilization for the transient Stokes' equations: stability and convergence analysis. SIAM Journal on Numerical Analysis, 2008, 47 (1), pp.409-439. ⟨10.1137/070707403⟩. ⟨inria-00178359v3⟩
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