Verification of Convergence Rates of Numerical Solutions for Parabolic Equations
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Jeong, Darae | - |
dc.contributor.author | Li, Yibao | - |
dc.contributor.author | Lee, Chaeyoung | - |
dc.contributor.author | Yang, Junxiang | - |
dc.contributor.author | Choi, Yongho | - |
dc.contributor.author | Kim, Junseok | - |
dc.date.accessioned | 2021-12-16T04:40:54Z | - |
dc.date.available | 2021-12-16T04:40:54Z | - |
dc.date.created | 2021-08-30 | - |
dc.date.issued | 2019 | - |
dc.identifier.issn | 1024-123X | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/131723 | - |
dc.description.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. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | HINDAWI LTD | - |
dc.subject | CAHN-HILLIARD EQUATION | - |
dc.subject | TUMOR-GROWTH | - |
dc.subject | 2ND-ORDER | - |
dc.subject | PHASE | - |
dc.subject | FIELD | - |
dc.subject | SCHEMES | - |
dc.subject | ENERGY | - |
dc.subject | MODEL | - |
dc.subject | TIME | - |
dc.subject | APPROXIMATIONS | - |
dc.title | Verification of Convergence Rates of Numerical Solutions for Parabolic Equations | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Kim, Junseok | - |
dc.identifier.doi | 10.1155/2019/8152136 | - |
dc.identifier.scopusid | 2-s2.0-85069042218 | - |
dc.identifier.wosid | 000474545100001 | - |
dc.identifier.bibliographicCitation | MATHEMATICAL PROBLEMS IN ENGINEERING, v.2019 | - |
dc.relation.isPartOf | MATHEMATICAL PROBLEMS IN ENGINEERING | - |
dc.citation.title | MATHEMATICAL PROBLEMS IN ENGINEERING | - |
dc.citation.volume | 2019 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Engineering | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Engineering, Multidisciplinary | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Interdisciplinary Applications | - |
dc.subject.keywordPlus | CAHN-HILLIARD EQUATION | - |
dc.subject.keywordPlus | TUMOR-GROWTH | - |
dc.subject.keywordPlus | 2ND-ORDER | - |
dc.subject.keywordPlus | PHASE | - |
dc.subject.keywordPlus | FIELD | - |
dc.subject.keywordPlus | SCHEMES | - |
dc.subject.keywordPlus | ENERGY | - |
dc.subject.keywordPlus | MODEL | - |
dc.subject.keywordPlus | TIME | - |
dc.subject.keywordPlus | APPROXIMATIONS | - |
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