Error estimates of finite element methods for nonlinear fractional stochastic differential equations

Yanpeng Zhang; Xiaoyuan Yang; Xiaocui Li

doi:10.1186/s13662-018-1665-0

Error estimates of finite element methods for nonlinear fractional stochastic differential equations

Yanpeng Zhang
, Xiaoyuan Yang
, Xiaocui Li^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper, we consider the Galerkin finite element approximations of the initial value problem for the nonlinear fractional stochastic partial differential equations with multiplicative noise. We study a spatial semidiscrete scheme with the standard Galerkin finite element method and a fully discrete scheme based on the Goreno–Mainardi–Moretti–Paradisi (GMMP) scheme. We establish strong convergence error estimates for both semidiscrete and fully discrete schemes.

Original language	English
Article number	215
Journal	Advances in Difference Equations
Volume	2018
Issue number	1
DOIs	https://doi.org/10.1186/s13662-018-1665-0
State	Published - 1 Dec 2018

Keywords

Error estimates
Finite element method
Initial value problem
Nonlinear fractional stochastic differential equations
Strong convergence

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10.1186/s13662-018-1665-0

Cite this

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title = "Error estimates of finite element methods for nonlinear fractional stochastic differential equations",

abstract = "In this paper, we consider the Galerkin finite element approximations of the initial value problem for the nonlinear fractional stochastic partial differential equations with multiplicative noise. We study a spatial semidiscrete scheme with the standard Galerkin finite element method and a fully discrete scheme based on the Goreno–Mainardi–Moretti–Paradisi (GMMP) scheme. We establish strong convergence error estimates for both semidiscrete and fully discrete schemes.",

keywords = "Error estimates, Finite element method, Initial value problem, Nonlinear fractional stochastic differential equations, Strong convergence",

author = "Yanpeng Zhang and Xiaoyuan Yang and Xiaocui Li",

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N2 - In this paper, we consider the Galerkin finite element approximations of the initial value problem for the nonlinear fractional stochastic partial differential equations with multiplicative noise. We study a spatial semidiscrete scheme with the standard Galerkin finite element method and a fully discrete scheme based on the Goreno–Mainardi–Moretti–Paradisi (GMMP) scheme. We establish strong convergence error estimates for both semidiscrete and fully discrete schemes.

AB - In this paper, we consider the Galerkin finite element approximations of the initial value problem for the nonlinear fractional stochastic partial differential equations with multiplicative noise. We study a spatial semidiscrete scheme with the standard Galerkin finite element method and a fully discrete scheme based on the Goreno–Mainardi–Moretti–Paradisi (GMMP) scheme. We establish strong convergence error estimates for both semidiscrete and fully discrete schemes.

KW - Error estimates

KW - Finite element method

KW - Initial value problem

KW - Nonlinear fractional stochastic differential equations

KW - Strong convergence

UR - https://www.scopus.com/pages/publications/85048890091

U2 - 10.1186/s13662-018-1665-0

DO - 10.1186/s13662-018-1665-0

M3 - 文章

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VL - 2018

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 215

ER -

Error estimates of finite element methods for nonlinear fractional stochastic differential equations

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Keywords

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