Strong Convergence of a Fully Discrete Scheme for Multiplicative Noise Driving SPDEs with Non-Globally Lipschitz Continuous Coefficients

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

Xu Yang

Weidong Zhao

  1. 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]