Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model

Handle URI:
http://hdl.handle.net/10754/563294
Title:
Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model
Authors:
Calo, Victor M. ( 0000-0002-1805-4045 ) ; Collier, Nathan; Niemi, Antti H.
Abstract:
We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is well-posed (stable) with a thickness-dependent constant in a norm encompassing the L2-norms of the bending moment, the shear force, the transverse deflection and the rotation vector. We then construct a numerical solution scheme based on quadrilateral scalar and vector finite elements of degree p. We show that for affine meshes the discretization inherits the stability of the continuous formulation provided that the optimal test functions are approximated by polynomials of degree p+3. We prove a theoretical error estimate in terms of the mesh size h and polynomial degree p and demonstrate numerical convergence on affine as well as non-affine mesh sequences. © 2013 Elsevier Ltd. All rights reserved.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program
Publisher:
Elsevier BV
Journal:
Computers & Mathematics with Applications
Issue Date:
Jan-2014
DOI:
10.1016/j.camwa.2013.07.012
ARXIV:
arXiv:1301.6149
Type:
Article
ISSN:
08981221
Additional Links:
http://arxiv.org/abs/arXiv:1301.6149v1
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorCalo, Victor M.en
dc.contributor.authorCollier, Nathanen
dc.contributor.authorNiemi, Antti H.en
dc.date.accessioned2015-08-03T11:45:05Zen
dc.date.available2015-08-03T11:45:05Zen
dc.date.issued2014-01en
dc.identifier.issn08981221en
dc.identifier.doi10.1016/j.camwa.2013.07.012en
dc.identifier.urihttp://hdl.handle.net/10754/563294en
dc.description.abstractWe analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is well-posed (stable) with a thickness-dependent constant in a norm encompassing the L2-norms of the bending moment, the shear force, the transverse deflection and the rotation vector. We then construct a numerical solution scheme based on quadrilateral scalar and vector finite elements of degree p. We show that for affine meshes the discretization inherits the stability of the continuous formulation provided that the optimal test functions are approximated by polynomials of degree p+3. We prove a theoretical error estimate in terms of the mesh size h and polynomial degree p and demonstrate numerical convergence on affine as well as non-affine mesh sequences. © 2013 Elsevier Ltd. All rights reserved.en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1301.6149v1en
dc.subjectDiscontinuous Petrov-Galerkinen
dc.subjectDiscrete stabilityen
dc.subjectError estimatesen
dc.subjectFinite element methoden
dc.subjectOptimal test functionsen
dc.subjectPlate bendingen
dc.titleAnalysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending modelen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.identifier.journalComputers & Mathematics with Applicationsen
dc.contributor.institutionAalto University, School of Engineering, Department of Civil and Structural Engineering, Espoo, Finlanden
dc.identifier.arxividarXiv:1301.6149en
kaust.authorCalo, Victor M.en
kaust.authorCollier, Nathanen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.