Discrete Besov framework for finite volume approximation of the p-laplacian on non-uniform cartesian grids
ESAIM. Proceedings, Tome 18 (2007), pp. 1-10
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This work addresses the problem of a priori error analysis for the finite volume approximation of solutions of the p-laplacian on cartesian grids. We first recall the way we constructed such schemes and the different error bounds we proved in our previous works. Then we concentrate particularly on the case where the exact solution has only weak regularity properties (which are natural for this problem) of Besov kind with derivation index in between 1 and 2. In this framework, the usual techniques to obtain error estimates for finite volumes schemes are not straightfoward to apply. Hence, we propose to take advantage of the variational structure of the equation and the schemes in order to obtain the error bounds. In the case of uniform meshes, this strategy was succesfully applied in [2] to obtain optimal estimates. We propose in this work to extend this approach to a more general family of quasi-uniform meshes.
Affiliations des auteurs :
Boris Andreianov 1 ; Franck Boyer 2 ; Florence Hubert 2
@article{EP_2007_18_a1,
author = {Boris Andreianov and Franck Boyer and Florence Hubert},
title = {Discrete {Besov} framework for finite volume approximation of the p-laplacian on non-uniform cartesian grids},
journal = {ESAIM. Proceedings},
pages = {1--10},
year = {2007},
volume = {18},
doi = {10.1051/proc:071801},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:071801/}
}
TY - JOUR AU - Boris Andreianov AU - Franck Boyer AU - Florence Hubert TI - Discrete Besov framework for finite volume approximation of the p-laplacian on non-uniform cartesian grids JO - ESAIM. Proceedings PY - 2007 SP - 1 EP - 10 VL - 18 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc:071801/ DO - 10.1051/proc:071801 LA - en ID - EP_2007_18_a1 ER -
%0 Journal Article %A Boris Andreianov %A Franck Boyer %A Florence Hubert %T Discrete Besov framework for finite volume approximation of the p-laplacian on non-uniform cartesian grids %J ESAIM. Proceedings %D 2007 %P 1-10 %V 18 %U http://geodesic.mathdoc.fr/articles/10.1051/proc:071801/ %R 10.1051/proc:071801 %G en %F EP_2007_18_a1
Boris Andreianov; Franck Boyer; Florence Hubert. Discrete Besov framework for finite volume approximation of the p-laplacian on non-uniform cartesian grids. ESAIM. Proceedings, Tome 18 (2007), pp. 1-10. doi: 10.1051/proc:071801
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