Acta mathematica Universitatis Comenianae, Tome 67 (1998) no. 1
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R. Eymard; M. Gutnic; D. Hilhorst. THE FINITE VOLUME METHOD FOR AN ELLIPTIC-PARABOLIC EQUATION. Acta mathematica Universitatis Comenianae, Tome 67 (1998) no. 1. http://geodesic.mathdoc.fr/item/AMUC_1998_67_1_a10/
@article{AMUC_1998_67_1_a10,
author = {R. Eymard and M. Gutnic and D. Hilhorst},
title = {THE {FINITE} {VOLUME} {METHOD} {FOR} {AN} {ELLIPTIC-PARABOLIC} {EQUATION}},
journal = {Acta mathematica Universitatis Comenianae},
year = {1998},
volume = {67},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_1998_67_1_a10/}
}
TY - JOUR
AU - R. Eymard
AU - M. Gutnic
AU - D. Hilhorst
TI - THE FINITE VOLUME METHOD FOR AN ELLIPTIC-PARABOLIC EQUATION
JO - Acta mathematica Universitatis Comenianae
PY - 1998
VL - 67
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_1998_67_1_a10/
ID - AMUC_1998_67_1_a10
ER -
%0 Journal Article
%A R. Eymard
%A M. Gutnic
%A D. Hilhorst
%T THE FINITE VOLUME METHOD FOR AN ELLIPTIC-PARABOLIC EQUATION
%J Acta mathematica Universitatis Comenianae
%D 1998
%V 67
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_1998_67_1_a10/
%F AMUC_1998_67_1_a10
In this note we prove the convergence of a finite volume scheme for the discretization of an elliptic-parabolic problem, namely the nonlinear diffusion equation $c(u)_t-\Delta u = 0$, together with Dirichlet boundary conditions and an initial condition. This is done by means of a priori estimates in $L^2$ and the use of Kolmogorov's theorem on relative compactness of subsets of $L^2$.
