| Issue |
ESAIM: M2AN
Volume 48, Number 1, January-February 2014
|
|
|---|---|---|
| Page(s) | 107 - 134 | |
| DOI | https://doi.org/10.1051/m2an/2013096 | |
| Published online | 18 December 2013 | |
Non linear schemes for the heat equation in 1D∗
1 LJLL, UPMC,
Paris,
France.
2 Laboratoire Jacques-Louis Lions
University Pierre et Marie Curie Boîte courrier 187 75252
Paris Cedex 05
France.
despres@ann.jussieu.fr
Received:
27
October
2012
Revised:
9
June
2013
Inspired by the growing use of non linear discretization techniques for the linear diffusion equation in industrial codes, we construct and analyze various explicit non linear finite volume schemes for the heat equation in dimension one. These schemes are inspired by the Le Potier’s trick [C. R. Acad. Sci. Paris, Ser. I 348 (2010) 691–695]. They preserve the maximum principle and admit a finite volume formulation. We provide a original functional setting for the analysis of convergence of such methods. In particular we show that the fourth discrete derivative is bounded in quadratic norm. Finally we construct, analyze and test a new explicit non linear maximum preserving scheme with third order convergence: it is optimal on numerical tests.
Mathematics Subject Classification: 65J05 / 65M08 / 65M12
Key words: Finite volume schemes / heat equation / non linear correction
The author acknowledges the support of ANR under contract ANR-12-BS01-0006-01. Moreover this work was carried out within the framework of the European Fusion Development Agreement and the French Research Federation for Fusion Studies. It is supported by the European Communities under the contract of Association between Euratom and CEA. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
© EDP Sciences, SMAI 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.