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Volume 35, Issue 3
Error Estimates of Finite Element Methods for Stochastic Fractional Differential Equations

Xiaocui Li & Xiaoyuan Yang

DOI: 10.4208/jcm.1607-m2015-0329

J. Comp. Math., 35 (2017), pp. 346-362.

Published online: 2017-06

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  • 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.

  • Keywords

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

  • AMS Subject Headings

60H15, 65M60, 60H35, 65M12.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

anny9702@126.com (Xiaocui Li)

xiaoyuanyang@vip.163.com (Xiaoyuan Yang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-35-346, author = {Li , Xiaocui and Yang , Xiaoyuan}, title = {Error Estimates of Finite Element Methods for Stochastic Fractional Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2017}, volume = {35}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1607-m2015-0329}, url = {http://global-sci.org/intro/article_detail/jcm/9776.html} }
TY - JOUR T1 - Error Estimates of Finite Element Methods for Stochastic Fractional Differential Equations AU - Li , Xiaocui AU - Yang , Xiaoyuan JO - Journal of Computational Mathematics VL - 3 SP - 346 EP - 362 PY - 2017 DA - 2017/06 SN - 35 DO - http://doi.org/10.4208/jcm.1607-m2015-0329 UR - https://global-sci.org/intro/article_detail/jcm/9776.html KW - Stochastic fractional differential equations, Finite element method, Error estimates, Strong convergence, Convolution quadrature. AB -

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.

Li , Xiaocui and Yang , Xiaoyuan. (2017). Error Estimates of Finite Element Methods for Stochastic Fractional Differential Equations. Journal of Computational Mathematics. 35 (3). 346-362. doi:10.4208/jcm.1607-m2015-0329
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