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A posteriori error estimation and adaptivity for degenerate parabolic problems. (English) Zbl 0942.65111
This paper develops a posteriori \(H_{-1}\) error bounds for a degenerate heat equation, and these are used in three adaptive-mesh strategies for a finite element method. Sample computations are presented for a problem with change of phase, in which the adaptive mesh captures the movement of the front. Front tracking is not used.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
80A22 Stefan problems, phase changes, etc.
35K65 Degenerate parabolic equations
35R35 Free boundary problems for PDEs
35K05 Heat equation
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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