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Adaptive finite element methods for parabolic problems. IV: Nonlinear Problems. (English) Zbl 0835.65116

Summary: [For part II see ibid. 32, No. 3, 706-740 (1995; Zbl 0830.65094).]
We extend our program on adaptive finite element methods for parabolic problems to a class of nonlinear scalar problems. We prove a posteriori error estimates, design corresponding adaptive algorithms, and present some numerical results.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
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