Strong Convergence of a Fully Discrete Scheme for Multiplicative Noise Driving SPDEs with Non-Globally Lipschitz Continuous Coefficients
Year: 2021
Author: Xu Yang, Weidong Zhao
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 4 : pp. 1085–1109
Abstract
This work investigates strong convergence of numerical schemes for nonlinear multiplicative noise driving stochastic partial differential equations under some weaker conditions imposed on the coefficients avoiding the commonly used global Lipschitz assumption in the literature. Space-time fully discrete scheme is proposed, which is performed by the finite element method in space and the implicit Euler method in time. Based on some technical lemmas including regularity properties for the exact solution of the considered problem, strong convergence analysis with sharp convergence rates for the proposed fully discrete scheme is rigorously established.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2020-0143
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 4 : pp. 1085–1109
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Stochastic partial differential equations strong convergence non-global Lipschitz finite element method variational solution mean square error estimate.
Author Details
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Strong optimal error estimates of discontinuous Galerkin method for multiplicative noise driving nonlinear SPDEs
Yang, Xu
Zhao, Weidong
Zhao, Wenju
Numerical Methods for Partial Differential Equations, Vol. 39 (2023), Iss. 3 P.2073
https://doi.org/10.1002/num.22958 [Citations: 1]