Error estimates for moving least square approximations

In this paper we obtain error estimates for moving least square approximations in the one-dimensional case. For the application of this method to the numerical solution of differential equations it is fundamental to have error estimates for the approximations of derivatives. We prove that, under app...

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Detalles Bibliográficos
Autores principales: Armentano, Maria Gabriela, Duran, Ricardo Guillermo
Publicado: 2001
Materias:
Convection-diffusion
Error estimates
Galerkin approximations
Moving least square
Differential equations
Error analysis
Galerkin methods
Problem solving
Theorem proving
Moving least square approximation
Least squares approximations
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01689274_v37_n3_p397_Armentano
http://hdl.handle.net/20.500.12110/paper_01689274_v37_n3_p397_Armentano
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_01689274_v37_n3_p397_Armentano
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spelling paper:paper_01689274_v37_n3_p397_Armentano2023-06-08T15:18:04Z Error estimates for moving least square approximations Armentano, Maria Gabriela Duran, Ricardo Guillermo Convection-diffusion Error estimates Galerkin approximations Moving least square Differential equations Error analysis Galerkin methods Problem solving Theorem proving Moving least square approximation Least squares approximations In this paper we obtain error estimates for moving least square approximations in the one-dimensional case. For the application of this method to the numerical solution of differential equations it is fundamental to have error estimates for the approximations of derivatives. We prove that, under appropriate hypothesis on the weight function and the distribution of points, the method produces optimal order approximations of the function and its first and second derivatives. As a consequence, we obtain optimal order error estimates for Galerkin approximations of coercive problems. Finally, as an application of the moving least square method we consider a convection-diffusion equation and propose a way of introducing up-wind by means of a non-symmetric weight function. We present several numerical results showing the good behavior of the method. © 2001 IMACS. Fil:Armentano, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2001 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01689274_v37_n3_p397_Armentano http://hdl.handle.net/20.500.12110/paper_01689274_v37_n3_p397_Armentano
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Convection-diffusion
Error estimates
Galerkin approximations
Moving least square
Differential equations
Error analysis
Galerkin methods
Problem solving
Theorem proving
Moving least square approximation
Least squares approximations
spellingShingle Convection-diffusion
Error estimates
Galerkin approximations
Moving least square
Differential equations
Error analysis
Galerkin methods
Problem solving
Theorem proving
Moving least square approximation
Least squares approximations
Armentano, Maria Gabriela
Duran, Ricardo Guillermo
Error estimates for moving least square approximations
topic_facet Convection-diffusion
Error estimates
Galerkin approximations
Moving least square
Differential equations
Error analysis
Galerkin methods
Problem solving
Theorem proving
Moving least square approximation
Least squares approximations
description In this paper we obtain error estimates for moving least square approximations in the one-dimensional case. For the application of this method to the numerical solution of differential equations it is fundamental to have error estimates for the approximations of derivatives. We prove that, under appropriate hypothesis on the weight function and the distribution of points, the method produces optimal order approximations of the function and its first and second derivatives. As a consequence, we obtain optimal order error estimates for Galerkin approximations of coercive problems. Finally, as an application of the moving least square method we consider a convection-diffusion equation and propose a way of introducing up-wind by means of a non-symmetric weight function. We present several numerical results showing the good behavior of the method. © 2001 IMACS.
author Armentano, Maria Gabriela
Duran, Ricardo Guillermo
author_facet Armentano, Maria Gabriela
Duran, Ricardo Guillermo
author_sort Armentano, Maria Gabriela
title Error estimates for moving least square approximations
title_short Error estimates for moving least square approximations
title_full Error estimates for moving least square approximations
title_fullStr Error estimates for moving least square approximations
title_full_unstemmed Error estimates for moving least square approximations
title_sort error estimates for moving least square approximations
publishDate 2001
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01689274_v37_n3_p397_Armentano
http://hdl.handle.net/20.500.12110/paper_01689274_v37_n3_p397_Armentano
work_keys_str_mv AT armentanomariagabriela errorestimatesformovingleastsquareapproximations
AT duranricardoguillermo errorestimatesformovingleastsquareapproximations
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