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| File | Size | Format | |
|---|---|---|---|
| 868667358.pdf | 596,4 kB | Adobe PDF | View/Open |
| Title: | Grad-div stabilization for the evolutionary Oseen problem with inf-sup stable finite elements |
| Authors: | Frutos, Javier de; García-Archilla, Bosco; John, Volker; Novo, Julia |
| URI: | https://doi.org/10.34657/2472 https://oa.tib.eu/renate/handle/123456789/3366 |
| Issue Date: | 2015 |
| Published in: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2112, ISSN 2198-5855 |
| Journal: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik |
| Volume: | 2112 |
| Publisher: | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik |
| 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 CrankNicolson 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 |
| Keywords: | time-dependent Oseen equations; inf-sup stable pairs of finite element spaces; grad-div stabilization; backward Euler scheme; two-step backward differentiation scheme (BDF2); Crank–Nicolson scheme; uniform error estimates |
| Type: | report; Text |
| Publishing status: | publishedVersion |
| DDC: | 510 |
| License: | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. |
| Appears in Collections: | Mathematik |
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Frutos, Javier de, Bosco García-Archilla, Volker John and Julia Novo, 2015. Grad-div stabilization for the evolutionary Oseen problem with inf-sup stable finite elements. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Frutos, J. d., García-Archilla, B., John, V. and Novo, J. (2015) Grad-div stabilization for the evolutionary Oseen problem with inf-sup stable finite elements. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Frutos J d, García-Archilla B, John V, Novo J. Grad-div stabilization for the evolutionary Oseen problem with inf-sup stable finite elements. Vol. 2112. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik; 2015.
Frutos, J. d., García-Archilla, B., John, V., & Novo, J. (2015). Grad-div stabilization for the evolutionary Oseen problem with inf-sup stable finite elements (Version publishedVersion, Vol. 2112). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Frutos J d, García-Archilla B, John V, Novo J. Grad-div stabilization for the evolutionary Oseen problem with inf-sup stable finite elements. Vol. 2112. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik; 2015.
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