CONVERGENCE ANALYSIS FOR A STABILIZED LINEAR SEMI-IMPLICIT NUMERICAL SCHEME FOR THE NONLOCAL CAHN-HILLIARD EQUATION

Xiao Li, Zhonghua Qiao, And Cheng Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)

Abstract

In this paper, we provide a detailed convergence analysis for a first order stabilized linear semi-implicit numerical scheme for the nonlocal Cahn— Hilliard equation, which follows from consistency and stability estimates for the numerical error function. Due to the complicated form of the nonlinear term, we adopt the discrete H-1 norm for the error function to establish the convergence result. In addition, the energy stability obtained by Du et al., [J. Comput. Phys. 363 (2018), pp. 39—54] requires an assumption on the uniform bound of the numerical solution, and such a bound is figured out in this paper by conducting the higher order consistency analysis. Taking the view that the numerical solution is indeed the exact solution with a perturbation, the error function is bounded uniformly under a loose constraint of the time step size, which then leads to the uniform maximum-norm bound of the numerical solution.

Original languageEnglish
Pages (from-to)171-188
Number of pages18
JournalMathematics of Computation
Volume90
Issue number327
DOIs
Publication statusPublished - Jan 2021

Keywords

  • convergence analysis
  • higher order consistency expansion.
  • Nonlocal Cahn—Hilliard equation
  • Stabilized linear scheme

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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