# 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} }

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…

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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

- MathematicsIMA 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…

An efficient explicit full-discrete scheme for strong approximation of stochastic Allen–Cahn equation

- Mathematics
- 2018

Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation

- MathematicsIMA 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 ScienceJ. 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

- Computer Science, MathematicsSIAM 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.

Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg–Landau equations

- MathematicsStochastic Processes and their Applications
- 2019

Spatial approximation of stochastic convolutions

- Computer Science, MathematicsJ. 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

- Mathematics
- 2003

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…