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Solution of nonlinear diffusion problems by linear approximation schemes. (English) Zbl 0792.65070

Authors’ summary: An approximation of degenerate parabolic problems (of porous medium and Stefan type) is studied. The enthalpy formulation and the variational technique are used. Nonstandard semidiscretisation in time is used and Newton-like iterations are applied to solve the corresponding elliptic problems. Some numerical experiments are discussed and compared to other methods and to analytic solutions.

MSC:

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations
76S05 Flows in porous media; filtration; seepage
80A22 Stefan problems, phase changes, etc.
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