TY - JOUR
T1 - Optimal Error Estimates of a Discontinuous Galerkin Method for Stochastic Allen-Cahn Equation Driven by Multiplicative Noise
AU - Yang , Xu
AU - Zhao , Weidong
AU - Zhao , Wenju
JO - Communications in Computational Physics
VL - 1
SP - 133
EP - 159
PY - 2024
DA - 2024/07
SN - 36
DO - http://doi.org/10.4208/cicp.OA-2023-0280
UR - https://global-sci.org/intro/article_detail/cicp/23299.html
KW - Stochastic Allen-Cahn equation, strong convergence, discontinuous Galerkin method, variational solution, multiplicative noise.
AB - <p style="text-align: justify;">In this paper, we develop and analyze an efficient discontinuous Galerkin
method for stochastic Allen-Cahn equation driven by multiplicative noise. The proposed method is realized by symmetric interior penalty discontinuous Galerkin finite
element method for space domain and implicit Euler method for time domain. Several new estimates and techniques are developed. Under some suitable regularity assumptions, we rigorously establish strong convergence results for the proposed fully
discrete numerical scheme and obtain optimal convergence rates in both space and
time. Numerical experiments are also carried out to validate our theoretical results
and demonstrate the effectiveness of the proposed method.</p>