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http://hdl.handle.net/10397/89597
Title: | Strong approximation of monotone stochastic partial differential equations driven by white noise | Authors: | Liu, Z Qiao, Z |
Issue Date: | Apr-2020 | Source: | IMA journal of numerical analysis, Apr. 2020, v. 40, no. 2, p. 1074-1093 | Abstract: | We establish an optimal strong convergence rate of a fully discrete numerical scheme for second-order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an additive space-time white noise. Our first step is to transform the original stochastic equation into an equivalent random equation whose solution possesses more regularity than the original one. Then we use the backward Euler in time and spectral Galerkin in space to fully discretise this random equation. By the monotonicity assumption, in combination with the factorisation method and stochastic calculus in martingale-type 2 Banach spaces, we derive a uniform maximum norm estimation and a Hölder-type regularity for both stochastic and random equations. Finally, the strong convergence rate of the proposed fully discrete scheme is obtained. Several numerical experiments are carried out to verify the theoretical result. | Keywords: | Backward Euler-spectral Galerkin scheme Martingale-type 2 Banach space Monotone stochastic partial differential equations Strong convergence rate |
Publisher: | Oxford University Press | Journal: | IMA journal of numerical analysis | ISSN: | 0272-4979 | EISSN: | 1464-3642 | DOI: | 10.1093/imanum/dry088 | Rights: | © The Author(s) 2019. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record Zhihui Liu, Zhonghua Qiao, Strong approximation of monotone stochastic partial differential equations driven by white noise, IMA Journal of Numerical Analysis, Volume 40, Issue 2, April 2020, Pages 1074–1093 is available online at: https://doi.org/10.1093/imanum/dry088. |
Appears in Collections: | Journal/Magazine Article |
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StrongApproxMonotoneSPDEWhiteNoise.pdf | Pre-Published version | 965.97 kB | Adobe PDF | View/Open |
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