TY - JOUR
T1 - Strong Convergence of a Fully Discrete Scheme for Multiplicative Noise Driving SPDEs with Non-Globally Lipschitz Continuous Coefficients
AU - Yang , Xu
AU - Zhao , Weidong
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1085
EP - 1109
PY - 2021
DA - 2021/09
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0143
UR - https://global-sci.org/intro/article_detail/nmtma/19531.html
KW - Stochastic partial differential equations, strong convergence, non-global Lipschitz,
finite element method, variational solution, mean square error estimate.
AB - <p style="text-align: justify;">This work investigates strong convergence of numerical schemes for nonlinear multiplicative noise driving stochastic partial differential equations under
some weaker conditions imposed on the coefficients avoiding the commonly used
global Lipschitz assumption in the literature. Space-time fully discrete scheme is
proposed, which is performed by the finite element method in space and the implicit
Euler method in time. Based on some technical lemmas including regularity properties for the exact solution of the considered problem, strong convergence analysis
with sharp convergence rates for the proposed fully discrete scheme is rigorously
established.</p>