L∞-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities
This paper deals with the finite element approximation of a class of variational inequalities (VI) and quasi-variational inequalities (QVI) with the right-hand side depending upon the solution. We prove that the approximation is optimally accurate in L∞ combining the Banach fixed point theorem with...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201010602 |
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| _version_ | 1832560913532583936 |
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| author | M. Boulbrachene P. Cortey-Dumont J. C. Miellou |
| author_facet | M. Boulbrachene P. Cortey-Dumont J. C. Miellou |
| author_sort | M. Boulbrachene |
| collection | DOAJ |
| description | This paper deals with the finite element approximation
of a class of variational inequalities (VI) and quasi-variational inequalities (QVI) with the right-hand
side depending upon the solution. We prove that the approximation is optimally accurate in L∞ combining the Banach fixed point theorem with the standard
uniform error estimates in linear VIs and QVIs. We also
prove that this approach extends successfully to the
corresponding noncoercive problems. |
| format | Article |
| id | doaj-art-edbe25201bff4c2cb293b880161008d4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-edbe25201bff4c2cb293b880161008d42025-02-03T01:26:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127530931910.1155/S0161171201010602L∞-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalitiesM. Boulbrachene0P. Cortey-Dumont1J. C. Miellou2Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Muscat 123, OmanDepartement de Marketing Scientifique, IBM, Tour Septentrion, La Défense, 92800 Puteaux, Paris, FranceLaboratoire de Calcul Scientifique, 16 Route de Gray, 25030 Besancon Cedex France, Paris, FranceThis paper deals with the finite element approximation of a class of variational inequalities (VI) and quasi-variational inequalities (QVI) with the right-hand side depending upon the solution. We prove that the approximation is optimally accurate in L∞ combining the Banach fixed point theorem with the standard uniform error estimates in linear VIs and QVIs. We also prove that this approach extends successfully to the corresponding noncoercive problems.http://dx.doi.org/10.1155/S0161171201010602 |
| spellingShingle | M. Boulbrachene P. Cortey-Dumont J. C. Miellou L∞-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities International Journal of Mathematics and Mathematical Sciences |
| title | L∞-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities |
| title_full | L∞-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities |
| title_fullStr | L∞-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities |
| title_full_unstemmed | L∞-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities |
| title_short | L∞-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities |
| title_sort | l∞ error estimates for a class of semilinear elliptic variational inequalities and quasi variational inequalities |
| url | http://dx.doi.org/10.1155/S0161171201010602 |
| work_keys_str_mv | AT mboulbrachene lerrorestimatesforaclassofsemilinearellipticvariationalinequalitiesandquasivariationalinequalities AT pcorteydumont lerrorestimatesforaclassofsemilinearellipticvariationalinequalitiesandquasivariationalinequalities AT jcmiellou lerrorestimatesforaclassofsemilinearellipticvariationalinequalitiesandquasivariationalinequalities |