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

Eriksson, Kenneth; Johnson, Claes

SIAM J. Numer. Anal. 32, No. 6, 1729-1749 (1995).

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

Keywords:

nonlinear parabolic problems; error control; adaptive finite element methods; error estimates; numerical results

Citations:

Zbl 0732.65093; Zbl 0835.65117; Zbl 0830.65094