Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations
- Authors: Sebastian Becker, Benjamin Gess, Arnulf Jentzen, Peter E. Kloeden
- Preprint year: 2018
- First public date: 2018-11-01
- arXiv: 1811.01725
- Status: Published
- Publication type: Journal article
- Publication year: 2020
- Journal: BIT : numerical mathematics, 60 (2020) 4, pp. 1057-1073
- DOI: 10.1007/s10543-020-00807-2
Abstract
Optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise are obtained. In particular, we establish the optimality of strong convergence rates for full-discrete approximations of stochastic Allen-Cahn equations with space-time white noise which have recently been obtained in [Becker, S., Gess, B., Jentzen, A., and Kloeden, P. E., Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations. arXiv:1711.02423 (2017)].