Abstract
This article establishes optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise. Thereby, this work proves the optimality of the strong convergence rates for certain full-discrete approximations of stochastic Allen–Cahn equations with space-time white noise which have been obtained in a recent previous work of the authors of this article.
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Acknowledgements
This work has been partially supported through the SNSF-Research project 200021_156603 “Numerical approximations of nonlinear stochastic ordinary and partial differential equations”. The third author acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Muenster: Dynamics-Geometry-Structure. Financial support by the DFG through the CRC 1283 “Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications” is acknowledged.
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Communicated by David Cohen.
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Becker, S., Gess, B., Jentzen, A. et al. Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations. Bit Numer Math 60, 1057–1073 (2020). https://doi.org/10.1007/s10543-020-00807-2
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DOI: https://doi.org/10.1007/s10543-020-00807-2