期刊
MATHEMATICAL PROBLEMS IN ENGINEERING
卷 2019, 期 -, 页码 -出版社
HINDAWI LTD
DOI: 10.1155/2019/8152136
关键词
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资金
- National Research Foundation of Korea (NRF) - Korea government (MSIP) [NRF-2017R1E1A1A03070953]
- Korea University Future Research Grant
- BK21 PLUS program
- National Research Foundation of Korea [21A20151613163] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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.
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