A general finite volume scheme for an elliptic-hyperbolic system using a variational approach

被引：0
|
作者：
M. R. Laydi
M. Ghilani
机构：
[1] Université de Franche-Comté,
[2] LCS URA CNRS 741,undefined
[3] 16,undefined
[4] route de Gray,undefined
[5] 25300 Besançon,undefined
[6] France.,undefined
[7] Université Moulay Ismail,undefined
[8] Faculté des Sciences,undefined
[9] BP 4010,undefined
[10] Beni M'hamed,undefined
[11] 50000 Meknès,undefined
[12] Maroc,undefined
来源：
Zeitschrift für angewandte Mathematik und Physik ZAMP | 1998年 / 49卷
关键词：
Key words. Elliptic, hyperbolic, finite volume scheme, finite element scheme, nodal method, variational method.;
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摘要：
We study the convergence of general finite volume schemes for the diphasic flow problem in porous media \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $u_t-{\rm div}(u\nabla p)=0$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\Delta p=0$\end{document} in a bounded domain. A general formula for the numerical flux on a triangular mesh is given. The stability and an estimate of the total variation of the approximate solutions are obtained by means of a variational method; the convergence follows easily for general data.
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页码：630 / 643
页数：13
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