Preprint 671-2000

Quantitative error estimates for the implicit Euler scheme for linear evolutionary problems with rough data.

Author(s) : Etienne Emmrich

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 671-2000

MSC 2000

65M15 Error bounds

65J10 Equations with linear operators

76D07 Stokes and related flows

34G10 Linear equations

Abstract :
For the initial-boundary value problem for a non-homogeneous linear parabolic differential equation with time-dependent coefficients, the discretization in time by the backward Euler method is considered. The method is shown to be convergent of first order even for rough data. Attention is directed, in particular, to estimates of the appearing constants as well as to restrictions on the step size in dependence on the problem's parameters. In addition, the temporal discretization of the incompressible Stokes problem and the dependence of the error on the Reynolds number is analysed.

Keywords : Linear parabolic PDE, parabolic smoothing, discretization in time, backward Euler, a priori error estimates, incompressible Stokes equation