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| File | Size | Format | |
|---|---|---|---|
| 787937630.pdf | 604,8 kB | Adobe PDF | View/Open |
| Title: | Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in 1D |
| Authors: | Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr |
| URI: | https://doi.org/10.34657/3208 https://oa.tib.eu/renate/handle/123456789/3072 |
| Issue Date: | 2014 |
| Published in: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1916, ISSN 2198-5855 |
| Journal: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik |
| Volume: | 1916 |
| Publisher: | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik |
| Abstract: | Algebraic flux correction schemes are nonlinear discretizations of convection dominated problems. In this work, a scheme from this class is studied for a steady-state convection-diffusion equation in one dimension. It is proved that this scheme satisfies the discrete maximum principle. Also, as it is a nonlinear scheme, the solvability of the linear subproblems arising in a Picard iteration is studied, where positive and negative results are proved. Furthermore, the non-existence of solutions for the nonlinear scheme is proved by means of counterexamples. Therefore, a modification of the method, which ensures the existence of a solution, is proposed. A weak version of the discrete maximum principle is proved for this modified method. |
| Keywords: | Finite element method; convection-diffusion equation; algebraic flux correction; discrete maximum principle; fixed point iteration; solvability of linear subproblems; solvability of nonlinear problem |
| Type: | Other; 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, 2014. Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in 1D. 2014. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Barrenechea, G. R., John, V. and Knobloch, P. (2014) “Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in 1D.” Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Barrenechea G R, John V, Knobloch P. Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in 1D. Vol. 1916. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik; 2014.
Barrenechea, G. R., John, V., & Knobloch, P. (2014). Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in 1D (Version publishedVersion, Vol. 1916). Version publishedVersion, Vol. 1916. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Barrenechea G R, John V, Knobloch P. Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in 1D. 2014;1916.
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