A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods
A posteriori error estimates for the generalized overlapping domain decomposition method (GODDM) (i.e., with Robin boundary conditions on the interfaces), for second order boundary value problems, are derived. We show that the error estimate in the continuous case depends on the differences of the t...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/947085 |
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| _version_ | 1849468757659877376 |
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| author | Hakima Benlarbi Ahmed-Salah Chibi |
| author_facet | Hakima Benlarbi Ahmed-Salah Chibi |
| author_sort | Hakima Benlarbi |
| collection | DOAJ |
| description | A posteriori error estimates for the generalized overlapping domain decomposition method (GODDM) (i.e., with Robin boundary conditions on the interfaces), for second order boundary value problems, are derived. We show that the error estimate in the continuous case depends on the differences of the traces of the subdomain solutions on the interfaces. After discretization of the domain by finite elements we use the techniques of the residual a posteriori error analysis to get an a posteriori error estimate for the discrete solutions on subdomains. The results of some numerical experiments are presented to support the theory. |
| format | Article |
| id | doaj-art-fe80386655b1470382e760945f0ca2c3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-fe80386655b1470382e760945f0ca2c32025-08-20T03:25:46ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/947085947085A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition MethodsHakima Benlarbi0Ahmed-Salah Chibi1Department of Mathematics, Badji Mokhtar University, B.P. 12, Annaba 23000, AlgeriaDepartment of Mathematics, Badji Mokhtar University, B.P. 12, Annaba 23000, AlgeriaA posteriori error estimates for the generalized overlapping domain decomposition method (GODDM) (i.e., with Robin boundary conditions on the interfaces), for second order boundary value problems, are derived. We show that the error estimate in the continuous case depends on the differences of the traces of the subdomain solutions on the interfaces. After discretization of the domain by finite elements we use the techniques of the residual a posteriori error analysis to get an a posteriori error estimate for the discrete solutions on subdomains. The results of some numerical experiments are presented to support the theory.http://dx.doi.org/10.1155/2012/947085 |
| spellingShingle | Hakima Benlarbi Ahmed-Salah Chibi A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods Journal of Applied Mathematics |
| title | A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods |
| title_full | A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods |
| title_fullStr | A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods |
| title_full_unstemmed | A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods |
| title_short | A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods |
| title_sort | posteriori error estimates for the generalized overlapping domain decomposition methods |
| url | http://dx.doi.org/10.1155/2012/947085 |
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