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Error Estimates of Finite Element Methods for Stochastic Fractional Differential Equations

Error Estimates of Finite Element Methods for Stochastic Fractional Differential Equations
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Year:    2017

Author:    Xiaocui Li, Xiaoyuan Yang

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 3 : pp. 346–362

Abstract

This paper studies the Galerkin finite element approximations of a class of stochastic fractional differential equations. The discretization in space is done by a standard continuous finite element method and almost optimal order error estimates are obtained. The discretization in time is achieved via the piecewise constant, discontinuous Galerkin method and a Laplace transform convolution quadrature. We give strong convergence error estimates for both semi-discrete and fully discrete schemes. The proof is based on the error estimates for the corresponding deterministic problem. Finally, the numerical example is carried out to verify the theoretical results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1607-m2015-0329

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 3 : pp. 346–362

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Stochastic fractional differential equations Finite element method Error estimates Strong convergence Convolution quadrature.

Author Details

Xiaocui Li

Xiaoyuan Yang

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