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.


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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