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Journal of Scientific Computing

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14-06-2015

Grad-div Stabilization for the Evolutionary Oseen Problem with Inf-sup Stable Finite Elements

Authors: Javier de Frutos, Bosco García-Archilla, Volker John, Julia Novo

Published in: Journal of Scientific Computing | Issue 3/2016

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Abstract

The approximation of the time-dependent Oseen problem using inf-sup stable mixed finite elements in a Galerkin method with grad-div stabilization is studied. The main goal is to prove that adding a grad-div stabilization term to the Galerkin approximation has a stabilizing effect for small viscosity. Both the continuous-in-time and the fully discrete case (backward Euler method, the two-step BDF, and Crank–Nicolson schemes) are analyzed. In fact, error bounds are obtained that do not depend on the inverse of the viscosity in the case where the solution is sufficiently smooth. The bounds for the divergence of the velocity as well as for the pressure are optimal. The analysis is based on the use of a specific Stokes projection. Numerical studies support the analytical results.

previous article Erratum to: A Stabilized Mixed Finite Element Method for Elliptic Optimal Control Problems

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Title: Grad-div Stabilization for the Evolutionary Oseen Problem with Inf-sup Stable Finite Elements
Authors: Javier de Frutos
Bosco García-Archilla
Volker John
Julia Novo
Publication date: 14-06-2015
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0052-1

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