Johnson, Claes; Nie, Yi-Yong; ThomĂ©e, Vidar An a posteriori error estimate and adaptive timestep control for a backward Euler discretization of a parabolic problem. (English) Zbl 0701.65063 SIAM J. Numer. Anal. 27, No. 2, 277-291 (1990). 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 Cited in 36 Documents 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 Keywords:algorithm; adaptive timestep control; backward Euler discretization; linear parabolic problem; a posteriori error estimate PDF BibTeX XML Cite \textit{C. Johnson} et al., SIAM J. Numer. Anal. 27, No. 2, 277--291 (1990; Zbl 0701.65063) Full Text: DOI OpenURL