Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES
We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic PDE on two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. Th...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/605140 |
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| author | A. Harbi M. Boulbrachene |
| author_facet | A. Harbi M. Boulbrachene |
| author_sort | A. Harbi |
| collection | DOAJ |
| description | We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic PDE on two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz asssumption on the nonlinearity, we establish, on each subdomain, an optimal L∞ error estimate between the discrete Schwarz sequence and the exact solution of the PDE. |
| format | Article |
| id | doaj-art-f4c538eec63e4ea78dd1ff4fa2245ec9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-f4c538eec63e4ea78dd1ff4fa2245ec92025-02-03T01:30:55ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/605140605140Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDESA. Harbi0M. Boulbrachene1Departement De Mathematiques, Universite Badji Mokhtar, Annaba 23000, AlgeriaDepartment of Mathematics & Statistics, Sultan Qaboos University, Muscat 123, OmanWe provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic PDE on two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz asssumption on the nonlinearity, we establish, on each subdomain, an optimal L∞ error estimate between the discrete Schwarz sequence and the exact solution of the PDE.http://dx.doi.org/10.1155/2011/605140 |
| spellingShingle | A. Harbi M. Boulbrachene Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES Journal of Applied Mathematics |
| title | Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES |
| title_full | Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES |
| title_fullStr | Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES |
| title_full_unstemmed | Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES |
| title_short | Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES |
| title_sort | maximum norm analysis of a nonmatching grids method for nonlinear elliptic pdes |
| url | http://dx.doi.org/10.1155/2011/605140 |
| work_keys_str_mv | AT aharbi maximumnormanalysisofanonmatchinggridsmethodfornonlinearellipticpdes AT mboulbrachene maximumnormanalysisofanonmatchinggridsmethodfornonlinearellipticpdes |