Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate
| ISSN: |
1069-8299
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|---|---|
| Keywords: |
Engineering ; Engineering General
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| Source: |
Wiley InterScience Backfile Collection 1832-2000
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| Topics: |
Mathematics
Technology
|
| Notes: |
In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
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| Additional Material: |
7 Ill.
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| Type of Medium: |
Electronic Resource
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| URL: |
| _version_ | 1798297777481973760 |
|---|---|
| addmaterial | 7 Ill. |
| autor | Wiberg, N.-E. Li, X. D. |
| autorsonst | Wiberg, N.-E. Li, X. D. |
| book_url | http://dx.doi.org/10.1002/cnm.1640100406 |
| datenlieferant | nat_lic_papers |
| hauptsatz | hsatz_simple |
| identnr | NLM163245134 |
| issn | 1069-8299 |
| journal_name | Communications in Numerical Methods in Engineering |
| materialart | 1 |
| notes | In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions. |
| package_name | Wiley-Blackwell |
| publikationsjahr_anzeige | 1994 |
| publikationsjahr_facette | 1994 |
| publikationsjahr_intervall | 8009:1990-1994 |
| publikationsjahr_sort | 1994 |
| publikationsort | Chichester |
| publisher | Wiley-Blackwell |
| reference | 10 (1994), S. 313-320 |
| schlagwort | Engineering Engineering General |
| search_space | articles |
| shingle_author_1 | Wiberg, N.-E. Li, X. D. |
| shingle_author_2 | Wiberg, N.-E. Li, X. D. |
| shingle_author_3 | Wiberg, N.-E. Li, X. D. |
| shingle_author_4 | Wiberg, N.-E. Li, X. D. |
| shingle_catch_all_1 | Wiberg, N.-E. Li, X. D. Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate Engineering Engineering General Engineering Engineering General In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions. 1069-8299 10698299 Wiley-Blackwell |
| shingle_catch_all_2 | Wiberg, N.-E. Li, X. D. Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate Engineering Engineering General Engineering Engineering General In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions. 1069-8299 10698299 Wiley-Blackwell |
| shingle_catch_all_3 | Wiberg, N.-E. Li, X. D. Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate Engineering Engineering General Engineering Engineering General In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions. 1069-8299 10698299 Wiley-Blackwell |
| shingle_catch_all_4 | Wiberg, N.-E. Li, X. D. Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate Engineering Engineering General Engineering Engineering General In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions. 1069-8299 10698299 Wiley-Blackwell |
| shingle_title_1 | Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate |
| shingle_title_2 | Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate |
| shingle_title_3 | Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate |
| shingle_title_4 | Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate |
| sigel_instance_filter | dkfz geomar wilbert ipn albert |
| source_archive | Wiley InterScience Backfile Collection 1832-2000 |
| timestamp | 2024-05-06T10:13:22.015Z |
| titel | Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate |
| titel_suche | Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate |
| topic | SA-SP ZG |
| uid | nat_lic_papers_NLM163245134 |