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A dG method for the Stokes equations related to nonconforming approximations

Roland Becker 1, 2 Daniela Capatina 1, 2 Julie Joie 1, 2, * 
* Corresponding author
2 CONCHA - Complex Flow Simulation Codes based on High-order and Adaptive methods
Inria Bordeaux - Sud-Ouest, UPPA - Université de Pau et des Pays de l'Adour, CNRS - Centre National de la Recherche Scientifique : UMR5142
Abstract : We study a discontinuous Galerkin method for the Stokes equations with a new stabilization of the viscous term. On the one hand, it allows us to recover, as the stabilization parameter tends towards infinity, some stable and well-known nonconforming approximations of the Stokes problem. On the other hand, we can easily define an a posteriori error indicator, based on the reconstruction of a locally conservative H(div)-tensor. An a priori error analysis is also carried out, yielding optimal convergence rates. Numerical tests illustrating the accuracy and the robustness of the scheme are presented.
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Submitted on : Thursday, July 30, 2009 - 11:29:48 AM
Last modification on : Friday, February 4, 2022 - 3:12:04 AM
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  • HAL Id : inria-00380772, version 3



Roland Becker, Daniela Capatina, Julie Joie. A dG method for the Stokes equations related to nonconforming approximations. [Research Report] 2009, pp.34. ⟨inria-00380772v3⟩



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