• Corpus ID: 238634812

# Strong convergence rates of a fully discrete scheme for nonlinear stochastic partial differential equations with non-globally Lipschitz coefficients driven by multiplicative noise

@article{Huang2021StrongCR,
title={Strong convergence rates of a fully discrete scheme for nonlinear stochastic partial differential equations with non-globally Lipschitz coefficients driven by multiplicative noise},
author={Can Huang and Jie Shen},
journal={ArXiv},
year={2021},
volume={abs/2110.05675}
}
• Published 12 October 2021
• Computer Science, Mathematics
• ArXiv
We consider a fully discrete scheme for nonlinear stochastic partial differential equations with non-globally Lipschitz coefficients driven by multiplicative noise in a multi-dimensional setting. Our method uses a polynomial based spectral method in space, so it does not require the elliptic operator A and the covariance operator Q of noise in the equation commute, and thus successfully alleviates a restriction of Fourier spectral method for SPDEs pointed out by Jentzen, Kloeden and Winkel in…

## References

SHOWING 1-10 OF 46 REFERENCES
Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities
• Mathematics
IMA Journal of Numerical Analysis
• 2019
In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous
Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations
• Mathematics
• 2017
The scientific literature contains a number of numerical approximation results for stochastic partial differential equations (SPDEs) with superlinearly growing nonlinearities but, to the best of our
Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation
• Mathematics
IMA Journal of Numerical Analysis
• 2018
This article analyses an explicit temporal splitting numerical scheme for the stochastic Allen–Cahn equation driven by additive noise in a bounded spatial domain with smooth boundary in dimension
Optimal Error Estimates of Galerkin Finite Element Methods for Stochastic Allen–Cahn Equation with Additive Noise
• Mathematics, Computer Science
J. Sci. Comput.
• 2019
By introducing two auxiliary approximation processes, an appropriate decomposition of the considered error terms is proposed and a novel approach of error analysis is introduced, to successfully recover the convergence rates of the numerical schemes.
Galerkin Finite Element Methods for Stochastic Parabolic Partial Differential Equations
• Yubin Yan
• Computer Science, Mathematics
SIAM J. Numer. Anal.
• 2005
Optimal strong convergence error estimates in the L2 and $\dot{H}^{-1}$ norms with respect to the spatial variable are obtained and the proof is based on appropriate nonsmooth data error estimates for the corresponding deterministic parabolic problem.
Spatial approximation of stochastic convolutions
• Computer Science, Mathematics
J. Comput. Appl. Math.
• 2011
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• Mathematics
• 2012
On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz
Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term
Abstract We study existence and uniqueness of a mild solution in the space of continuous functions and existence of an invariant measure for a class of reaction-diffusion systems on bounded domains