Approximation of degenerate parabolic problems using numerical integration. (English) Zbl 0655.65131

Nochetto, Ricardo H.; Verdi, Claudio

SIAM J. Numer. Anal. 25, No. 4, 784-814 (1988).

A class of multidimensional degenerate parabolic equations is considered: the two-phase Stefan problem and the porous medium equation are analyzed as models of singular parabolic equations; nonstationary filtration (with gravity) is also treated as a model of elliptic-parabolic equations. A fully discrete scheme combined with a smoothing procedure (when needed) is proposed.

Reviewer: M.A.Ibiejugba

MSC:

65Z05	Applications to the sciences
65N15	Error bounds for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35K55	Nonlinear parabolic equations
35K65	Degenerate parabolic equations
35R35	Free boundary problems for PDEs

Keywords:

two-phase Stefan problem; porous medium equation; singular parabolic equations; nonstationary filtration; fully discrete scheme; smoothing procedure