ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 65, 35 Thalhammer, Mechthild, University of Innsbruck, Austria Non-smooth data error estimates for linearly implicit Runge-Kutta methods and applications We consider linearly implicit one-step methods for time discretization of semilinear parabolic equations with nonsmooth initial data and derive finitetime error bounds. The analysis is based on the framework of analytic semigroups which includes reaction-diffusion equations and incompressible Navier-Stokes equations. Such error bounds are used in the study of the long-time behaviour of numerical discretizations applied to parabolic problems. Reference: A. Ostermann and M. Thalhammer: Non-smooth data error estimates for linearly implicit Runge-Kutta methods and applications, in preparation.