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The finite volume method for an elliptic-parabolic equation. (English) Zbl 0930.35082

A nonlinear diffusion problem with Dirichlet boundary condition is investigated in this paper especially from a numerical point of view. An approximate solution of this problem is constructed via finite volume scheme and existence of unique solution of this numerical solution is proved. The convergence of the approximate solution to the weak solution of this problem is presented. 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 \(L_2\).

MSC:

35K55 Nonlinear parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76S05 Flows in porous media; filtration; seepage
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