An Immersed Virtual Element Method Based on Interface Problems
An immersed virtual element method is developed to solve the second-order interface problems in two-dimensional space , which overcomes the problem that the constructed space cannot satisfy both the coordination and jump conditions. The key idea is to use the conforming virtual element spaces on...
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| Format: | Article |
| Language: | Chinese |
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Harbin University of Science and Technology Publications
2023-12-01
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| Series: | Journal of Harbin University of Science and Technology |
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| Online Access: | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2287 |
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| _version_ | 1839626748069675008 |
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| author | MA Jun chi SUO Yu yang |
| author_facet | MA Jun chi SUO Yu yang |
| author_sort | MA Jun chi |
| collection | DOAJ |
| description |
An immersed virtual element method is developed to solve the second-order interface problems in two-dimensional space , which overcomes the problem that the constructed space cannot satisfy both the coordination and jump conditions. The key idea is to use the conforming virtual element spaces on a shape regular background unfitted mesh for discretization, and project them to the immersed finite element spaces on interface elements which are cut by the interfaces from the background mesh, making the proposed method combine the advantages of both body-fitted mesh methods and unfitted mesh methods. Then the strict theoretical derivation and optimal error estimation of the method are given. Finally, the numerical example is solved. By calculating the L2 and H1 norms of the numerical solution and analytical solution, and making the linear regression diagram of errors, the method achieves second order convergence in the L2 norm and first order convergence in the H1 norm, indicating that the theoretical analysis results are correct. |
| format | Article |
| id | doaj-art-b56e018c438f4c11a9cf8f8c4f4865b1 |
| institution | Matheson Library |
| issn | 1007-2683 |
| language | zho |
| publishDate | 2023-12-01 |
| publisher | Harbin University of Science and Technology Publications |
| record_format | Article |
| series | Journal of Harbin University of Science and Technology |
| spelling | doaj-art-b56e018c438f4c11a9cf8f8c4f4865b12025-07-17T03:58:19ZzhoHarbin University of Science and Technology PublicationsJournal of Harbin University of Science and Technology1007-26832023-12-01280614515310.15938/j.jhust.2023.06.017An Immersed Virtual Element Method Based on Interface ProblemsMA Jun chi0SUO Yu yang1SchoolofMathematics,LiaoningNormalUniversity,Dalian116029,ChinaSchoolofMathematics,LiaoningNormalUniversity,Dalian116029,China An immersed virtual element method is developed to solve the second-order interface problems in two-dimensional space , which overcomes the problem that the constructed space cannot satisfy both the coordination and jump conditions. The key idea is to use the conforming virtual element spaces on a shape regular background unfitted mesh for discretization, and project them to the immersed finite element spaces on interface elements which are cut by the interfaces from the background mesh, making the proposed method combine the advantages of both body-fitted mesh methods and unfitted mesh methods. Then the strict theoretical derivation and optimal error estimation of the method are given. Finally, the numerical example is solved. By calculating the L2 and H1 norms of the numerical solution and analytical solution, and making the linear regression diagram of errors, the method achieves second order convergence in the L2 norm and first order convergence in the H1 norm, indicating that the theoretical analysis results are correct.https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2287elliptic interface problemvirtual element methodimmersed finite element methodoptimal error estimates |
| spellingShingle | MA Jun chi SUO Yu yang An Immersed Virtual Element Method Based on Interface Problems Journal of Harbin University of Science and Technology elliptic interface problem virtual element method immersed finite element method optimal error estimates |
| title | An Immersed Virtual Element Method Based on Interface Problems |
| title_full | An Immersed Virtual Element Method Based on Interface Problems |
| title_fullStr | An Immersed Virtual Element Method Based on Interface Problems |
| title_full_unstemmed | An Immersed Virtual Element Method Based on Interface Problems |
| title_short | An Immersed Virtual Element Method Based on Interface Problems |
| title_sort | immersed virtual element method based on interface problems |
| topic | elliptic interface problem virtual element method immersed finite element method optimal error estimates |
| url | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2287 |
| work_keys_str_mv | AT majunchi animmersedvirtualelementmethodbasedoninterfaceproblems AT suoyuyang animmersedvirtualelementmethodbasedoninterfaceproblems AT majunchi immersedvirtualelementmethodbasedoninterfaceproblems AT suoyuyang immersedvirtualelementmethodbasedoninterfaceproblems |