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dc.contributor.author
Apel, Thomas  
dc.contributor.author
Lombardi, Ariel Luis  
dc.contributor.author
Winkler, Max  
dc.date.available
2018-02-06T19:14:35Z  
dc.date.issued
2014-08  
dc.identifier.citation
Apel, Thomas; Lombardi, Ariel Luis; Winkler, Max; Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω); EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 48; 4; 8-2014; 1117-1145  
dc.identifier.issn
0764-583X  
dc.identifier.uri
http://hdl.handle.net/11336/35857  
dc.description.abstract
The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. Anisotropic, graded meshes from a former paper are reused for dealing with the singular behaviour of the solution in the vicinity of the non-smooth parts of the boundary. The discretization error is analyzed for the piecewise linear approximation in the H1(Ω)- and L2(Ω)-norms by using a new quasi-interpolation operator. This new interpolant is introduced in order to prove the estimates for L2(Ω)-data in the differential equation which is not possible for the standard nodal interpolant. These new estimates allow for the extension of certain error estimates for optimal control problems with elliptic partial differential equations and for a simpler proof of the discrete compactness property for edge elements of any order on this kind of finite element meshes.  
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
Finite Element Method  
dc.subject
Edfe And Corner Singularities  
dc.subject
Anisotropic Mesh Grading  
dc.subject
Elliptic Boundary Value Problem  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω)  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2018-02-05T20:15:10Z  
dc.journal.volume
48  
dc.journal.number
4  
dc.journal.pagination
1117-1145  
dc.journal.pais
Francia  
dc.journal.ciudad
Paris  
dc.description.fil
Fil: Apel, Thomas. Universität der Bundeswehr München; Alemania  
dc.description.fil
Fil: Lombardi, Ariel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Universidad de Buenos Aires; Argentina  
dc.description.fil
Fil: Winkler, Max. Universität der Bundeswehr München; Alemania  
dc.journal.title
Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/1303.2960.pdf  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1051/m2an/2013134  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.esaim-m2an.org/articles/m2an/abs/2014/04/m2an130134/m2an130134.html