Difference schemes for degenerate parabolic equations

Socolovsky, E. A.

doi:10.1090/S0025-5718-1986-0856694-0

Difference schemes for degenerate parabolic equations
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Math. Comp. 47 (1986), 411-420 Request permission

Abstract:

Diagonal dominant implicit-difference schemes approximating a porous media type class of multidimensional nonlinear equations are shown to generate semigroups in an approximate ${L^1}$-space, and the rate of convergence to the semigroup solution in ${L^1}$ is given. The numerical schemes proposed by Berger et al. in [4] are described and a proof of convergence for the fully discrete algorithms is outlined. Numerical experiments are discussed.

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On Numerical Methods for Degenerate Parabolic Problems