THE FINITE VOLUME METHOD FOR AN ELLIPTIC-PARABOLIC EQUATION
Robert Eymard, Michaël Gutnic, Dorothea Hilhorst · 1998
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 \\Gamma \\Deltau = 0, together with Dirichlet boundary conditions and an initial condition. This is done by means of a priori estimates in L² and the use of Kolmogorov's theorem on relative compactness of subsets of L².