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dc.contributor.author
Bonito, Andrea
dc.contributor.author
Cascón, José Manuel
dc.contributor.author
Mekchay, Khamron
dc.contributor.author
Morin, Pedro
dc.contributor.author
Nochetto, Ricardo Horacio
dc.date.available
2019-02-26T21:52:03Z
dc.date.issued
2016-12
dc.identifier.citation
Bonito, Andrea; Cascón, José Manuel; Mekchay, Khamron; Morin, Pedro; Nochetto, Ricardo Horacio; High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates; Springer; Foundations Of Computational Mathematics; 16; 6; 12-2016; 1473-1539
dc.identifier.issn
1615-3375
dc.identifier.uri
http://hdl.handle.net/11336/70885
dc.description.abstract
We present a new AFEM for the Laplace–Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally W∞1 and piecewise in a suitable Besov class embedded in C1 , α with α∈ (0 , 1 ]. The idea is to have the surface sufficiently well resolved in W∞1 relative to the current resolution of the PDE in H1. This gives rise to a conditional contraction property of the PDE module. We present a suitable approximation class and discuss its relation to Besov regularity of the surface, solution, and forcing. We prove optimal convergence rates for AFEM which are dictated by the worst decay rate of the surface error in W∞1 and PDE error in H1.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
A Posteriori Error Estimates
dc.subject
Adaptive Finite Element Method
dc.subject
Convergence Rates
dc.subject
Higher Order
dc.subject
Laplace–Beltrami Operator
dc.subject
Parametric Surfaces
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2019-02-25T18:47:04Z
dc.identifier.eissn
1615-3383
dc.journal.volume
16
dc.journal.number
6
dc.journal.pagination
1473-1539
dc.journal.pais
Alemania
dc.journal.ciudad
Berlin
dc.description.fil
Fil: Bonito, Andrea. Texas A&M University; Estados Unidos
dc.description.fil
Fil: Cascón, José Manuel. Universidad de Salamanca; España
dc.description.fil
Fil: Mekchay, Khamron. Chulalongkorn University; Tailandia
dc.description.fil
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral; Argentina
dc.description.fil
Fil: Nochetto, Ricardo Horacio. University of Maryland; Estados Unidos
dc.journal.title
Foundations Of Computational Mathematics
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s10208-016-9335-7
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s10208-016-9335-7
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1511.05019
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