A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces

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In this article we develop a posteriori error estimates for second order linear elliptic problems with point sources in two- and three-dimensional domains. We prove a global upper bound and a local lower bound for the error measured in a weighted Sobolev space. The weight considered is a (positive)...

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Autores principales: Agnelli, Juan Pablo, Garau, Eduardo Mario, Morin, Pedro
Formato: article
Lenguaje:Inglés
Publicado: 2021
Materias:
Elliptic problems
Point sources
A posteriori error estimates
Finite elements
Weighted Sobolev spaces
Acceso en línea:http://hdl.handle.net/11086/20821
https://doi.org/10.1051/m2an/2014010
Aporte de:
Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba
id I10-R141-11086-20821
record_format dspace
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Elliptic problems
Point sources
A posteriori error estimates
Finite elements
Weighted Sobolev spaces
spellingShingle Elliptic problems
Point sources
A posteriori error estimates
Finite elements
Weighted Sobolev spaces
Agnelli, Juan Pablo
Garau, Eduardo Mario
Morin, Pedro
A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
topic_facet Elliptic problems
Point sources
A posteriori error estimates
Finite elements
Weighted Sobolev spaces
description In this article we develop a posteriori error estimates for second order linear elliptic problems with point sources in two- and three-dimensional domains. We prove a global upper bound and a local lower bound for the error measured in a weighted Sobolev space. The weight considered is a (positive) power of the distance to the support of the Dirac delta source term, and belongs to the Muckenhoupt’s class A2. The theory hinges on local approximation properties of either Clément or Scott–Zhang interpolation operators, without need of modifications, and makes use of weighted estimates for fractional integrals and maximal functions. Numerical experiments with an adaptive algorithm yield optimal meshes and very good effectivity indices.
format article
author Agnelli, Juan Pablo
Garau, Eduardo Mario
Morin, Pedro
author_facet Agnelli, Juan Pablo
Garau, Eduardo Mario
Morin, Pedro
author_sort Agnelli, Juan Pablo
title A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
title_short A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
title_full A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
title_fullStr A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
title_full_unstemmed A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
title_sort posteriori error estimates for elliptic problems with dirac measure terms in weighted spaces
publishDate 2021
url http://hdl.handle.net/11086/20821
https://doi.org/10.1051/m2an/2014010
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AT morinpedro aposteriorierrorestimatesforellipticproblemswithdiracmeasuretermsinweightedspaces
AT agnellijuanpablo posteriorierrorestimatesforellipticproblemswithdiracmeasuretermsinweightedspaces
AT garaueduardomario posteriorierrorestimatesforellipticproblemswithdiracmeasuretermsinweightedspaces
AT morinpedro posteriorierrorestimatesforellipticproblemswithdiracmeasuretermsinweightedspaces
bdutipo_str Repositorios
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