Local boundary estimates for the Lagrange multiplier discretization of a Dirichlet boundary value problem with application to domain decomposition
Abstract We give an estimate on the error resulting from approximating the outer normal derivative of the solution of a second-order partial differential equation with the Lagrange multiplier obtained in using the Lagrange multiplier method for imposing the Dirichlet boundary conditions. We consider...
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Gespeichert in:
| Autor*in: |
Bertoluzza, Silvia [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2006 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2006 |
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| Übergeordnetes Werk: |
Enthalten in: Calcolo - Springer-Verlag, 1964, 43(2006), 3 vom: Sept., Seite 121-149 |
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| Übergeordnetes Werk: |
volume:43 ; year:2006 ; number:3 ; month:09 ; pages:121-149 |
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| DOI / URN: |
10.1007/s10092-006-0115-7 |
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OLC2069160777 |
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| 520 | |a Abstract We give an estimate on the error resulting from approximating the outer normal derivative of the solution of a second-order partial differential equation with the Lagrange multiplier obtained in using the Lagrange multiplier method for imposing the Dirichlet boundary conditions. We consider both the case of smooth domains and, in view of an application in the framework of domain decomposition, the case of polygonal domains. The estimate given, supported by numerical results, shows that the mesh in the interior of the (sub)domain can be chosen more coarsely than near the boundary, when only a good approximation of the outer normal derivative is needed, as in the case of the evaluation of the Steklov-Poincaré operator, or when solving with a Schur complement approach the linear system arising from the three-fields domain decomposition method. Keywords: Lagrange multipliers, error estimate, normal derivative, Steklov-Poincaré operator | ||
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| 650 | 4 | |a Domain Decomposition Method | |
| 650 | 4 | |a Smooth Domain | |
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10.1007/s10092-006-0115-7 doi (DE-627)OLC2069160777 (DE-He213)s10092-006-0115-7-p DE-627 ger DE-627 rakwb eng 510 VZ Bertoluzza, Silvia verfasserin aut Local boundary estimates for the Lagrange multiplier discretization of a Dirichlet boundary value problem with application to domain decomposition 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract We give an estimate on the error resulting from approximating the outer normal derivative of the solution of a second-order partial differential equation with the Lagrange multiplier obtained in using the Lagrange multiplier method for imposing the Dirichlet boundary conditions. We consider both the case of smooth domains and, in view of an application in the framework of domain decomposition, the case of polygonal domains. The estimate given, supported by numerical results, shows that the mesh in the interior of the (sub)domain can be chosen more coarsely than near the boundary, when only a good approximation of the outer normal derivative is needed, as in the case of the evaluation of the Steklov-Poincaré operator, or when solving with a Schur complement approach the linear system arising from the three-fields domain decomposition method. Keywords: Lagrange multipliers, error estimate, normal derivative, Steklov-Poincaré operator Domain Decomposition Domain Decomposition Method Smooth Domain Lagrange Multiplier Method Polygonal Domain Enthalten in Calcolo Springer-Verlag, 1964 43(2006), 3 vom: Sept., Seite 121-149 (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:43 year:2006 number:3 month:09 pages:121-149 https://doi.org/10.1007/s10092-006-0115-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4277 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4700 AR 43 2006 3 09 121-149 |
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10.1007/s10092-006-0115-7 doi (DE-627)OLC2069160777 (DE-He213)s10092-006-0115-7-p DE-627 ger DE-627 rakwb eng 510 VZ Bertoluzza, Silvia verfasserin aut Local boundary estimates for the Lagrange multiplier discretization of a Dirichlet boundary value problem with application to domain decomposition 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract We give an estimate on the error resulting from approximating the outer normal derivative of the solution of a second-order partial differential equation with the Lagrange multiplier obtained in using the Lagrange multiplier method for imposing the Dirichlet boundary conditions. We consider both the case of smooth domains and, in view of an application in the framework of domain decomposition, the case of polygonal domains. The estimate given, supported by numerical results, shows that the mesh in the interior of the (sub)domain can be chosen more coarsely than near the boundary, when only a good approximation of the outer normal derivative is needed, as in the case of the evaluation of the Steklov-Poincaré operator, or when solving with a Schur complement approach the linear system arising from the three-fields domain decomposition method. Keywords: Lagrange multipliers, error estimate, normal derivative, Steklov-Poincaré operator Domain Decomposition Domain Decomposition Method Smooth Domain Lagrange Multiplier Method Polygonal Domain Enthalten in Calcolo Springer-Verlag, 1964 43(2006), 3 vom: Sept., Seite 121-149 (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:43 year:2006 number:3 month:09 pages:121-149 https://doi.org/10.1007/s10092-006-0115-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4277 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4700 AR 43 2006 3 09 121-149 |
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10.1007/s10092-006-0115-7 doi (DE-627)OLC2069160777 (DE-He213)s10092-006-0115-7-p DE-627 ger DE-627 rakwb eng 510 VZ Bertoluzza, Silvia verfasserin aut Local boundary estimates for the Lagrange multiplier discretization of a Dirichlet boundary value problem with application to domain decomposition 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract We give an estimate on the error resulting from approximating the outer normal derivative of the solution of a second-order partial differential equation with the Lagrange multiplier obtained in using the Lagrange multiplier method for imposing the Dirichlet boundary conditions. We consider both the case of smooth domains and, in view of an application in the framework of domain decomposition, the case of polygonal domains. The estimate given, supported by numerical results, shows that the mesh in the interior of the (sub)domain can be chosen more coarsely than near the boundary, when only a good approximation of the outer normal derivative is needed, as in the case of the evaluation of the Steklov-Poincaré operator, or when solving with a Schur complement approach the linear system arising from the three-fields domain decomposition method. Keywords: Lagrange multipliers, error estimate, normal derivative, Steklov-Poincaré operator Domain Decomposition Domain Decomposition Method Smooth Domain Lagrange Multiplier Method Polygonal Domain Enthalten in Calcolo Springer-Verlag, 1964 43(2006), 3 vom: Sept., Seite 121-149 (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:43 year:2006 number:3 month:09 pages:121-149 https://doi.org/10.1007/s10092-006-0115-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4277 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4700 AR 43 2006 3 09 121-149 |
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10.1007/s10092-006-0115-7 doi (DE-627)OLC2069160777 (DE-He213)s10092-006-0115-7-p DE-627 ger DE-627 rakwb eng 510 VZ Bertoluzza, Silvia verfasserin aut Local boundary estimates for the Lagrange multiplier discretization of a Dirichlet boundary value problem with application to domain decomposition 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract We give an estimate on the error resulting from approximating the outer normal derivative of the solution of a second-order partial differential equation with the Lagrange multiplier obtained in using the Lagrange multiplier method for imposing the Dirichlet boundary conditions. We consider both the case of smooth domains and, in view of an application in the framework of domain decomposition, the case of polygonal domains. The estimate given, supported by numerical results, shows that the mesh in the interior of the (sub)domain can be chosen more coarsely than near the boundary, when only a good approximation of the outer normal derivative is needed, as in the case of the evaluation of the Steklov-Poincaré operator, or when solving with a Schur complement approach the linear system arising from the three-fields domain decomposition method. Keywords: Lagrange multipliers, error estimate, normal derivative, Steklov-Poincaré operator Domain Decomposition Domain Decomposition Method Smooth Domain Lagrange Multiplier Method Polygonal Domain Enthalten in Calcolo Springer-Verlag, 1964 43(2006), 3 vom: Sept., Seite 121-149 (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:43 year:2006 number:3 month:09 pages:121-149 https://doi.org/10.1007/s10092-006-0115-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4277 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4700 AR 43 2006 3 09 121-149 |
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10.1007/s10092-006-0115-7 doi (DE-627)OLC2069160777 (DE-He213)s10092-006-0115-7-p DE-627 ger DE-627 rakwb eng 510 VZ Bertoluzza, Silvia verfasserin aut Local boundary estimates for the Lagrange multiplier discretization of a Dirichlet boundary value problem with application to domain decomposition 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract We give an estimate on the error resulting from approximating the outer normal derivative of the solution of a second-order partial differential equation with the Lagrange multiplier obtained in using the Lagrange multiplier method for imposing the Dirichlet boundary conditions. We consider both the case of smooth domains and, in view of an application in the framework of domain decomposition, the case of polygonal domains. The estimate given, supported by numerical results, shows that the mesh in the interior of the (sub)domain can be chosen more coarsely than near the boundary, when only a good approximation of the outer normal derivative is needed, as in the case of the evaluation of the Steklov-Poincaré operator, or when solving with a Schur complement approach the linear system arising from the three-fields domain decomposition method. Keywords: Lagrange multipliers, error estimate, normal derivative, Steklov-Poincaré operator Domain Decomposition Domain Decomposition Method Smooth Domain Lagrange Multiplier Method Polygonal Domain Enthalten in Calcolo Springer-Verlag, 1964 43(2006), 3 vom: Sept., Seite 121-149 (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:43 year:2006 number:3 month:09 pages:121-149 https://doi.org/10.1007/s10092-006-0115-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4277 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4700 AR 43 2006 3 09 121-149 |
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Local boundary estimates for the Lagrange multiplier discretization of a Dirichlet boundary value problem with application to domain decomposition |
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Abstract We give an estimate on the error resulting from approximating the outer normal derivative of the solution of a second-order partial differential equation with the Lagrange multiplier obtained in using the Lagrange multiplier method for imposing the Dirichlet boundary conditions. We consider both the case of smooth domains and, in view of an application in the framework of domain decomposition, the case of polygonal domains. The estimate given, supported by numerical results, shows that the mesh in the interior of the (sub)domain can be chosen more coarsely than near the boundary, when only a good approximation of the outer normal derivative is needed, as in the case of the evaluation of the Steklov-Poincaré operator, or when solving with a Schur complement approach the linear system arising from the three-fields domain decomposition method. Keywords: Lagrange multipliers, error estimate, normal derivative, Steklov-Poincaré operator © Springer-Verlag 2006 |
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Abstract We give an estimate on the error resulting from approximating the outer normal derivative of the solution of a second-order partial differential equation with the Lagrange multiplier obtained in using the Lagrange multiplier method for imposing the Dirichlet boundary conditions. We consider both the case of smooth domains and, in view of an application in the framework of domain decomposition, the case of polygonal domains. The estimate given, supported by numerical results, shows that the mesh in the interior of the (sub)domain can be chosen more coarsely than near the boundary, when only a good approximation of the outer normal derivative is needed, as in the case of the evaluation of the Steklov-Poincaré operator, or when solving with a Schur complement approach the linear system arising from the three-fields domain decomposition method. Keywords: Lagrange multipliers, error estimate, normal derivative, Steklov-Poincaré operator © Springer-Verlag 2006 |
| abstract_unstemmed |
Abstract We give an estimate on the error resulting from approximating the outer normal derivative of the solution of a second-order partial differential equation with the Lagrange multiplier obtained in using the Lagrange multiplier method for imposing the Dirichlet boundary conditions. We consider both the case of smooth domains and, in view of an application in the framework of domain decomposition, the case of polygonal domains. The estimate given, supported by numerical results, shows that the mesh in the interior of the (sub)domain can be chosen more coarsely than near the boundary, when only a good approximation of the outer normal derivative is needed, as in the case of the evaluation of the Steklov-Poincaré operator, or when solving with a Schur complement approach the linear system arising from the three-fields domain decomposition method. Keywords: Lagrange multipliers, error estimate, normal derivative, Steklov-Poincaré operator © Springer-Verlag 2006 |
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Local boundary estimates for the Lagrange multiplier discretization of a Dirichlet boundary value problem with application to domain decomposition |
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