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|---|---|---|---|
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| Title: | A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations |
| Authors: | Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr |
| URI: | https://doi.org/10.34657/1834 https://oa.tib.eu/renate/handle/123456789/1784 |
| Issue Date: | 2012 |
| Published in: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik, Volume 1690, ISSN 0946-8633 |
| Journal: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik |
| Volume: | 1690 |
| Publisher: | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik |
| Abstract: | An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations. |
| Keywords: | Finite element method; local projection stabilization; crosswind diffusion; convection-diffusion-reaction equation; well posedness; time dependent problem; stability; 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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Barrenechea, Gabriel R., Volker John and Petr Knobloch, 2012. A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Barrenechea, G. R., John, V. and Knobloch, P. (2012) A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Barrenechea G R, John V, Knobloch P. A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations. Vol. 1690. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik; 2012.
Barrenechea, G. R., John, V., & Knobloch, P. (2012). A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations (Version publishedVersion, Vol. 1690). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Barrenechea G R, John V, Knobloch P. A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations. Vol. 1690. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik; 2012.
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