A Consistent Immersed Finite Element Method for the Interface Elasticity Problems
We propose a new scheme for elasticity problems having discontinuity in the coefficients. In the previous work (Kwak et al., 2014), the authors suggested a method for solving such problems by finite element method using nonfitted grids. The proposed method is based on the P1-nonconforming finite ele...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/3292487 |
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| _version_ | 1832554576744546304 |
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| author | Sangwon Jin Do Y. Kwak Daehyeon Kyeong |
| author_facet | Sangwon Jin Do Y. Kwak Daehyeon Kyeong |
| author_sort | Sangwon Jin |
| collection | DOAJ |
| description | We propose a new scheme for elasticity problems having discontinuity in the coefficients. In the previous work (Kwak et al., 2014), the authors suggested a method for solving such problems by finite element method using nonfitted grids. The proposed method is based on the P1-nonconforming finite element methods with stabilizing terms. In this work, we modify the method by adding the consistency terms, so that the estimates of consistency terms are not necessary. We show optimal error estimates in H1 and divergence norms under minimal assumptions. Various numerical experiments also show optimal rates of convergence. |
| format | Article |
| id | doaj-art-87e2f103fdac4a2da4f5de009c0f10cd |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-87e2f103fdac4a2da4f5de009c0f10cd2025-02-03T05:51:10ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/32924873292487A Consistent Immersed Finite Element Method for the Interface Elasticity ProblemsSangwon Jin0Do Y. Kwak1Daehyeon Kyeong2Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of KoreaKorea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of KoreaKorea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of KoreaWe propose a new scheme for elasticity problems having discontinuity in the coefficients. In the previous work (Kwak et al., 2014), the authors suggested a method for solving such problems by finite element method using nonfitted grids. The proposed method is based on the P1-nonconforming finite element methods with stabilizing terms. In this work, we modify the method by adding the consistency terms, so that the estimates of consistency terms are not necessary. We show optimal error estimates in H1 and divergence norms under minimal assumptions. Various numerical experiments also show optimal rates of convergence.http://dx.doi.org/10.1155/2016/3292487 |
| spellingShingle | Sangwon Jin Do Y. Kwak Daehyeon Kyeong A Consistent Immersed Finite Element Method for the Interface Elasticity Problems Advances in Mathematical Physics |
| title | A Consistent Immersed Finite Element Method for the Interface Elasticity Problems |
| title_full | A Consistent Immersed Finite Element Method for the Interface Elasticity Problems |
| title_fullStr | A Consistent Immersed Finite Element Method for the Interface Elasticity Problems |
| title_full_unstemmed | A Consistent Immersed Finite Element Method for the Interface Elasticity Problems |
| title_short | A Consistent Immersed Finite Element Method for the Interface Elasticity Problems |
| title_sort | consistent immersed finite element method for the interface elasticity problems |
| url | http://dx.doi.org/10.1155/2016/3292487 |
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