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

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


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
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