✦ LIBER ✦
Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: nonsmooth-data error estimates and applications to long-time behaviour
✍ Scribed by Christian Lubich; Alexander Ostermann
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 713 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0168-9274
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✦ Synopsis
We derive error bounds for Runge-Kutta time discretizations of semilinear parabolic equations with nonsmooth initial data. The framework includes reaction-diffusion equations and the incompressible Navier-Stokes equations. Nonsmooth-data error bounds of the type given here are needed in the study of the long-time behaviour of numerical discretizations. As an illustration, we use these low-order error bounds in proving high-order convergence of invariant closed curves of a Runge-Kutta method to periodic orbits of the parabolic problem.