A robust nonconforming H-2-element
Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counterexample is given...
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| Format: | Journal Article |
| Language: | English |
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2009
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| Online Access: | https://hdl.handle.net/10356/91499 http://hdl.handle.net/10220/6056 http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ELSEVIER_SCOPUS&id=doi:&genre=&isbn=&issn=&date=2001&volume=70&issue=234&spage=489&epage=505&aulast=Nilssen&aufirst=%20T%20K&auinit=&title=Mathematics%20of%20Computation&atitle=A%20robust%20nonconforming%20H. |
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| author | Nilssen, Trygve K. Tai, Xue Cheng Winther, Ragnar |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Nilssen, Trygve K. Tai, Xue Cheng Winther, Ragnar |
| author_sort | Nilssen, Trygve K. |
| collection | NTU |
| description | Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counterexample is given to show that the Morley method diverges for the reduced second order equation. As an alternative to the Morley element we propose to use a nonconforming H-2-element which is H-1-conforming. We show that the new finite element method converges in the energy norm uniformly in the perturbation parameter. |
| first_indexed | 2024-10-01T07:44:53Z |
| format | Journal Article |
| id | ntu-10356/91499 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:44:53Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | ntu-10356/914992023-02-28T19:37:34Z A robust nonconforming H-2-element Nilssen, Trygve K. Tai, Xue Cheng Winther, Ragnar School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counterexample is given to show that the Morley method diverges for the reduced second order equation. As an alternative to the Morley element we propose to use a nonconforming H-2-element which is H-1-conforming. We show that the new finite element method converges in the energy norm uniformly in the perturbation parameter. Published version 2009-08-12T03:16:58Z 2019-12-06T18:06:46Z 2009-08-12T03:16:58Z 2019-12-06T18:06:46Z 2000 2000 Journal Article Nilssen, T. K., Tan, X. C., & Winther R.(2000). A robust nonconforming H-2-element. Mathematics of Computation, 70(234), 489-505. 0025-5718 https://hdl.handle.net/10356/91499 http://hdl.handle.net/10220/6056 http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ELSEVIER_SCOPUS&id=doi:&genre=&isbn=&issn=&date=2001&volume=70&issue=234&spage=489&epage=505&aulast=Nilssen&aufirst=%20T%20K&auinit=&title=Mathematics%20of%20Computation&atitle=A%20robust%20nonconforming%20H. 10.1090/S0025-5718-00-01230-8 en Mathematics of Computation. Mathematics of Computation © copyright 2000 American Mathematical Society. The journal's website is located at http://www.ams.org/mcom/. 17 p. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis Nilssen, Trygve K. Tai, Xue Cheng Winther, Ragnar A robust nonconforming H-2-element |
| title | A robust nonconforming H-2-element |
| title_full | A robust nonconforming H-2-element |
| title_fullStr | A robust nonconforming H-2-element |
| title_full_unstemmed | A robust nonconforming H-2-element |
| title_short | A robust nonconforming H-2-element |
| title_sort | robust nonconforming h 2 element |
| topic | DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis |
| url | https://hdl.handle.net/10356/91499 http://hdl.handle.net/10220/6056 http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ELSEVIER_SCOPUS&id=doi:&genre=&isbn=&issn=&date=2001&volume=70&issue=234&spage=489&epage=505&aulast=Nilssen&aufirst=%20T%20K&auinit=&title=Mathematics%20of%20Computation&atitle=A%20robust%20nonconforming%20H. |
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