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.
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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.
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