An a posteriori error estimate and adaptive timestep control for a backward Euler discretization of a parabolic problem. (English) Zbl 0701.65063

Johnson, Claes; Nie, Yi-Yong; Thomée, Vidar

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

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