Verification of Convergence Rates of Numerical Solutions for Parabolic Equations

Darae Jeong, Yibao Li, Chaeyoung Lee, Junxiang Yang, Yongho Choi, Junseok Kim

Research output: Contribution to journalArticle

Abstract

In this paper, we propose a verification method for the convergence rates of the numerical solutions for parabolic equations. Specifically, we consider the numerical convergence rates of the heat equation, the Allen-Cahn equation, and the Cahn-Hilliard equation. Convergence test results show that if we refine the spatial and temporal steps at the same time, then we have the second-order convergence rate for the second-order scheme. However, in the case of the first-order in time and the second-order in space scheme, we may have the first-order or the second-order convergence rates depending on starting spatial and temporal step sizes. Therefore, for a rigorous numerical convergence test, we need to perform the spatial and the temporal convergence tests separately.

Original languageEnglish
Article number8152136
JournalMathematical Problems in Engineering
Volume2019
DOIs
Publication statusPublished - 2019 Jan 1

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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