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Volume 31, Issue 2
An LDG Method for Stochastic Cahn-Hilliard Type Equation Driven by General Multiplicative Noise Involving Second-Order Derivative

Li Zhou & Yunzhang Li

DOI: 10.4208/cicp.OA-2021-0134

Commun. Comput. Phys., 31 (2022), pp. 516-547.

Published online: 2022-01

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  • 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.

  • Keywords

Local discontinuous Galerkin method, stochastic Cahn-Hilliard type equations, multiplicative noise, stability analysis, error estimates.

  • AMS Subject Headings

65C30, 60H35

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-31-516, author = {Zhou , Li and Li , Yunzhang}, title = {An LDG Method for Stochastic Cahn-Hilliard Type Equation Driven by General Multiplicative Noise Involving Second-Order Derivative}, journal = {Communications in Computational Physics}, year = {2022}, volume = {31}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0134}, url = {http://global-sci.org/intro/article_detail/cicp/20214.html} }
TY - JOUR T1 - An LDG Method for Stochastic Cahn-Hilliard Type Equation Driven by General Multiplicative Noise Involving Second-Order Derivative AU - Zhou , Li AU - Li , Yunzhang JO - Communications in Computational Physics VL - 2 SP - 516 EP - 547 PY - 2022 DA - 2022/01 SN - 31 DO - http://doi.org/10.4208/cicp.OA-2021-0134 UR - https://global-sci.org/intro/article_detail/cicp/20214.html KW - Local discontinuous Galerkin method, stochastic Cahn-Hilliard type equations, multiplicative noise, stability analysis, error estimates. AB -

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.

Zhou , Li and Li , Yunzhang. (2022). An LDG Method for Stochastic Cahn-Hilliard Type Equation Driven by General Multiplicative Noise Involving Second-Order Derivative. Communications in Computational Physics. 31 (2). 516-547. doi:10.4208/cicp.OA-2021-0134
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