Verification of Convergence Rates of Numerical Solutions for Parabolic Equations
Joint Authors
Jeong, Darae
Kim, Junseok
Choi, Yongho
Li, Yibao
Lee, Chaeyoung
Yang, Junxiang
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-06-23
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Jeong, Darae& Li, Yibao& Lee, Chaeyoung& Yang, Junxiang& Choi, Yongho& Kim, Junseok. 2019. Verification of Convergence Rates of Numerical Solutions for Parabolic Equations. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1197373
Modern Language Association (MLA)
Jeong, Darae…[et al.]. Verification of Convergence Rates of Numerical Solutions for Parabolic Equations. Mathematical Problems in Engineering No. 2019 (2019), pp.1-10.
https://search.emarefa.net/detail/BIM-1197373
American Medical Association (AMA)
Jeong, Darae& Li, Yibao& Lee, Chaeyoung& Yang, Junxiang& Choi, Yongho& Kim, Junseok. Verification of Convergence Rates of Numerical Solutions for Parabolic Equations. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1197373
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1197373