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This paper focuses on investigating the density convergence of a fully discrete finite difference method when applied to numerically solve the stochastic Cahn--Hilliard equation driven by multiplicative space-time white noises. The main…

Numerical Analysis · Mathematics 2026-03-06 Jialin Hong , Diancong Jin , Derui Sheng

The stochastic Cahn-Hilliard equation driven by a fractional Brownian sheet provides a more accurate model for correlated space-time random perturbations. This study delves into two key aspects: first, it rigorously examines the regularity…

Numerical Analysis · Mathematics 2026-02-16 Nan Deng , Wanrong Cao

In this article, we develop and analyze a full discretization, based on the spatial spectral Galerkin method and the temporal drift implicit Euler scheme, for the stochastic Cahn--Hilliard equation driven by multiplicative space-time white…

Numerical Analysis · Mathematics 2020-06-22 Jianbo Cui , Jialin Hong

We consider the stochastic Cahn-Hilliard equation driven by additive Gaussian noise in a convex domain with polygonal boundary in dimension $d\le 3$. We discretize the equation using a standard finite element method in space and a fully…

Numerical Analysis · Mathematics 2018-05-04 Daisuke Furihata , Mihály Kovács , Stig Larsson , Fredrik Lindgren

In this paper, we propose and analyze an explicit time-stepping scheme for a spatial discretization of stochastic Cahn--Hilliard equation with additive noise. The fully discrete approximation combines a spectral Galerkin method in space…

Numerical Analysis · Mathematics 2023-08-31 Meng Cai , Ruisheng Qi , Xiaojie Wang

In two recent publications [Kov{\'a}cs, Larsson, and Mesforush, SIAM J. Numer. Anal. 49(6), 2407-2429, 2011] and [Furihata, et al., SIAM J. Numer. Anal. 56(2), 708-731, 2018], strong convergence of the semi-discrete and fully discrete…

Numerical Analysis · Mathematics 2020-06-16 Ruisheng Qi , Xiaojie Wang

This paper develops and analyzes some fully discrete mixed finite element methods for the stochastic Cahn-Hilliard equation with gradient-type multiplicative noise that is white in time and correlated in space. The stochastic Cahn-Hilliard…

Numerical Analysis · Mathematics 2019-03-14 Xiaobing Feng , Yukun Li , Yi Zhang

Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…

Numerical Analysis · Mathematics 2020-08-04 Ruisheng Qi , Xiaojie Wang

In this article, we consider the stochastic Cahn--Hilliard equation driven by space-time white noise. We discretize this equation by using a spatial spectral Galerkin method and a temporal accelerated implicit Euler method. The optimal…

Numerical Analysis · Mathematics 2020-06-23 Jianbo Cui , Jialin Hong , Liying Sun

In this work, we establish the Freidlin--Wentzell large deviations principle (LDP) of the stochastic Cahn--Hilliard equation with small noise, which implies the one-point LDP. Further, we give the one-point LDP of the spatial finite…

Numerical Analysis · Mathematics 2026-03-06 Diancong Jin , Derui Sheng

In this paper, we consider a new approach for semi-discretization in time and spatial discretization of a class of semi-linear stochastic partial differential equations (SPDEs) with multiplicative noise. The drift term of the SPDEs is only…

Numerical Analysis · Mathematics 2023-07-10 Yukun Li , Liet Vo , Guanqian Wang

We study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn--Hilliard equations with cubic nonlinearity and driven by additive noise. The spatial (resp. temporal) discretization is performed…

Numerical Analysis · Mathematics 2022-07-20 Charles-Edouard Bréhier , Jianbo Cui , Xiaojie Wang

We prove a weak rate of convergence of a fully discrete scheme for stochastic Cahn--Hilliard equation with additive noise, where the spectral Galerkin method is used in space and the backward Euler method is used in time. Compared with the…

Numerical Analysis · Mathematics 2023-03-21 Meng Cai , Siqing Gan , Yaozhong Hu

This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…

Numerical Analysis · Mathematics 2018-11-22 Xiaobing Feng , Yukun Li , Yi Zhang

This paper proposes and analyzes a novel fully discrete finite element scheme with the interpolation operator for stochastic Cahn-Hilliard equations with functional-type noise. The nonlinear term satisfies a one-side Lipschitz condition and…

Numerical Analysis · Mathematics 2023-06-27 Yukun Li , Corey Prachniak , Yi Zhang

Strong and weak approximation errors of a spatial finite element method are analyzed for stochastic partial differential equations(SPDEs) with one-sided Lipschitz coefficients, including the stochastic Allen--Cahn equation, driven by…

Probability · Mathematics 2019-06-03 Jianbo Cui , Jialin Hong

In this paper, we consider the numerical approximation of a time-fractional stochastic Cahn--Hilliard equation driven by an additive fractionally integrated Gaussian noise. The model involves a Caputo fractional derivative in time of order…

Numerical Analysis · Mathematics 2024-02-07 Mariam Al-Maskari , Samir Karaa

We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an…

Numerical Analysis · Mathematics 2020-05-21 Zhihui Liu , Zhonghua Qiao

A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite…

Numerical Analysis · Mathematics 2025-02-07 Nils Bullerjahn

In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order $\alpha \in (0,1)$ in a…

Numerical Analysis · Mathematics 2015-10-27 Samir Karaa , Kassem Mustapha , Amiya K. Pani
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