Strong Convergence of Full Discretization for Stochastic Cahn-Hilliard Equation Driven by Additive Noise

Jialin Hong, Liying Sun, Jianbo Cui

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)

Abstract

In this article, we consider the stochastic Cahn-Hilliard equation driven by additive noise. We discretize the equation by exploiting the spectral Galerkin method in space and a temporal accelerated implicit Euler method. Based on optimal regularity estimates of both exact and numerical solutions, we prove that the proposed numerical method is strongly convergent with a sharp convergence rate in a negative Sobolev space. Utilizing the semigroup theory and interpolation inequality, we deduce the spatial optimal convergence rate and the temporal superconvergence rate of the proposed numerical method in the strong sense.

Original languageEnglish
Pages (from-to)2866-2899
Number of pages34
JournalSIAM Journal on Numerical Analysis
Volume59
Issue number6
DOIs
Publication statusPublished - Jan 2021

Keywords

  • accelarated implicit Euler method
  • spectral Galerkin method
  • stochastic Cahn-Hilliard equation
  • strong convergence rate

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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