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

Erik Burman 1 Miguel Angel Fernández 2
2 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
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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SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2008, 47 (1), pp.409-439. 〈10.1137/070707403〉
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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, Society for Industrial and Applied Mathematics, 2008, 47 (1), pp.409-439. 〈10.1137/070707403〉. 〈inria-00178359v3〉

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