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 - <p style="text-align: justify;">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.</p>