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dc.contributor.author
Cejas, María Eugenia
dc.contributor.author
Duran, Ricardo Guillermo
dc.contributor.author
Prieto, Mariana Ines
dc.date.available
2021-06-29T23:02:17Z
dc.date.issued
2021-02-26
dc.identifier.citation
Cejas, María Eugenia; Duran, Ricardo Guillermo; Prieto, Mariana Ines; Mixed methods for degenerate elliptic problems and application to fractional Laplacian; EDP Sciences; ESAIM. Modélisation mathématique et analyse numérique; 55; 26-2-2021; 993-1019
dc.identifier.issn
0764-583X
dc.identifier.uri
http://hdl.handle.net/11336/135120
dc.description.abstract
We analyze the approximation by mixed finite element methods of solutions of equations of the form −div (a∇u) = g, where the coefficient a = a(x) can degenerate going to zero or infinity. First, we extend the classic error analysis to this case provided that the coefficient a belongs to the Muckenhoupt class A2. The analysis developed applies to general mixed finite element spaces satisfying the standard commutative diagram property, whenever some stability and interpolation error estimates are valid in weighted norms. Next, we consider in detail the case of Raviart–Thomas spaces of arbitrary order, obtaining optimal order error estimates for simplicial elements in any dimension and for convex quadrilateral elements in the two dimensional case, in both cases under a regularity assumption on the family of meshes. For the lowest order case we show that the regularity assumption can be removed and prove anisotropic error estimates which are of interest in problems with boundary layers. Finally we apply the results to a problem arising in the solution of the fractional Laplace equation.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
EDP Sciences
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
DEGENERATE ELLIPTIC PROBLEMS
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FRACTIONAL LAPLACIAN
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MIXED FINITE ELEMENTS
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Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Mixed methods for degenerate elliptic problems and application to fractional Laplacian
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2021-06-10T19:26:03Z
dc.identifier.eissn
1290-3841
dc.journal.volume
55
dc.journal.pagination
993-1019
dc.journal.pais
Francia
dc.description.fil
Fil: Cejas, María Eugenia. Universidad Nacional de La Plata. Departamento de Matemática, Facultad de Ciencias Exactas. Centro de Matemática La Plata ; Argentina
dc.description.fil
Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
dc.description.fil
Fil: Prieto, Mariana Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
dc.journal.title
ESAIM. Modélisation mathématique et analyse numérique
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.esaim-m2an.org/articles/m2an/abs/2021/01/m2an200082/m2an200082.html
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info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1051/m2an/2020068
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1903.05138
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