An LDG Method for Stochastic Cahn-Hilliard Type Equation Driven by General Multiplicative Noise Involving Second-Order Derivative
Year: 2022
Author: Li Zhou, Yunzhang Li
Communications in Computational Physics, Vol. 31 (2022), Iss. 2 : pp. 516–547
Abstract
In this paper, we propose a local discontinuous Galerkin (LDG) method for the multi-dimensional stochastic Cahn-Hilliard type equation in a general form, which involves second-order derivative $∆u$ in the multiplicative noise. The stability of our scheme is proved for arbitrary polygonal domain with triangular meshes. We get the sub-optimal error estimate $\mathbb{O}(h^k)$ if the Cartesian meshes with $Q^k$ elements are used. Numerical examples are given to display the performance of the LDG method.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0134
Communications in Computational Physics, Vol. 31 (2022), Iss. 2 : pp. 516–547
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Local discontinuous Galerkin method stochastic Cahn-Hilliard type equations multiplicative noise stability analysis error estimates.
Author Details
-
Asymptotics of large deviations of finite difference method for stochastic Cahn–Hilliard equation
Jin, Diancong | Sheng, DeruiActa Mathematica Scientia, Vol. 45 (2025), Iss. 3 P.1078
https://doi.org/10.1007/s10473-025-0318-0 [Citations: 0] -
Strong optimal error estimates of discontinuous Galerkin method for multiplicative noise driving nonlinear SPDEs
Yang, Xu | Zhao, Weidong | Zhao, WenjuNumerical Methods for Partial Differential Equations, Vol. 39 (2023), Iss. 3 P.2073
https://doi.org/10.1002/num.22958 [Citations: 1] -
Density convergence of a fully discrete finite difference method for stochastic Cahn–Hilliard equation
Hong, Jialin | Jin, Diancong | Sheng, DeruiMathematics of Computation, Vol. 93 (2023), Iss. 349 P.2215
https://doi.org/10.1090/mcom/3928 [Citations: 2]