A Comparative Numerical Study Of Different Finite Element Formulations For 2d Model Elliptic Problems: Continuous And Discontinuous Galerkin, Mixed And Hybrid Methods

dc.creatorForti
dc.creatorTiago L. D.; Farias
dc.creatorAgnaldo M.; Devloo
dc.creatorPhilippe R. B.; Gomes
dc.creatorSonia M.
dc.date2016
dc.dateagos
dc.date2017-11-13T13:54:58Z
dc.date2017-11-13T13:54:58Z
dc.date.accessioned2018-03-29T06:08:27Z
dc.date.available2018-03-29T06:08:27Z
dc.identifierFinite Elements In Analysis And Design . Elsevier Science Bv, v. 115, p. 9 - 20, 2016.
dc.identifier0168-874X
dc.identifier1872-6925
dc.identifierWOS:000373562300002
dc.identifier10.1016/j.finel.2016.02.009
dc.identifierhttp://www-sciencedirect-com.ez88.periodicos.capes.gov.br/science/article/pii/S0168874X16300270?via%3Dihub
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/329542
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1366567
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.descriptionIn this work, different finite element formulations for elliptic problems are implemented and compared, in terms of accuracy versus number of required degrees of freedom. The implemented formulations are: (a) the classical H-1 weak formulation (continuous); (b) the non-symmetric discontinuous Galerkin formulation by Baumann, Oden and Babuska; (c) a mixed discontinuous Galerkin formulation, known as Local Discontinuous Galerkin (LDG); (d) a mixed H(div)-conforming formulation; (e) a primal hybrid formulation. In order to compare the methods, two 2-dimensional test problems are approximated, one having a smooth solution and the second one presenting a square root singularity in a boundary node. The different formulations are compared in terms of the L-2 norm of the approximation errors in the solution and in its gradient (the flux). The tests are performed with h refinement with constant order of approximation p, as well as for a given hp refinement procedure. For the problem with a smooth solution, the results confirm convergence orders predicted by theoretical a priori error estimates. As expected, the application of hp refinement to the singular problem improves considerably the performance of all methods. Furthermore, due to the type of the singularity (square root), the efficiency of continuous and discontinuous Galerkin formulations is further improved by using enriched spaces with quarter-point elements. Regarding continuous, hybrid and mixed formulations, the effect of using static condensation of element equations is also analysed, in order to illustrate the reduction in the global system of equations in each case. A third comparison is given in terms of the conservation of the flux over a curve around a singularity. (C) 2016 Elsevier B.V. All rights reserved.
dc.description115
dc.description9
dc.description20
dc.descriptionBrazilian National Agency of Petroleum, Natural Gas and Biofuels (ANP - PETROBRAS)
dc.descriptionCNPq - Brazilian Research Council
dc.descriptionCAPES Foundation within Ministry of Education in Brazil
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.languageEnglish
dc.publisherElsevier Science BV
dc.publisherAmsterdam
dc.relationFinite Elements in Analysis and Design
dc.rightsfechado
dc.sourceWOS
dc.subjectFinite Elements
dc.subjectDiscontinuous Galerkin
dc.subjectH(div) Spaces
dc.subjectHybrid Method
dc.subjectHp Refinements
dc.subjectQuarter-point Elements
dc.subjectElliptic Singular Problem
dc.titleA Comparative Numerical Study Of Different Finite Element Formulations For 2d Model Elliptic Problems: Continuous And Discontinuous Galerkin, Mixed And Hybrid Methods
dc.typeArtículos de revistas


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