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An a posteriori error estimate and adaptive timestep control for a backward Euler discretization of a parabolic problem. (English) Zbl 0701.65063
Authors’ summary: A simple algorithm for adaptive timestep control is presented for a backward Euler discretization of a linear parabolic problem. The algorithm is based on an a posteriori error estimate involving the computed approximate solution. It is proved, that with only very rough a priori information on the exact solution, the algorithm will choose a sequence of timesteps for which the error will be controlled (up to a constant) uniformly in time on a given tolerance level.
Reviewer: J.D.P.Donnelly

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
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