Stability, convergence, and accuracy of a new finite element method for the circular arch problem
type: Item
instance of: scholarly article
title: Stability, convergence, and accuracy of a new finite element method for the circular arch problem
zbMATH Open document ID: 0607.73077
DOI: 10.1016/0045-7825(87)90074-0
author: Isidoro Miranda
author: Abimael F. D. Loula
author: Leopoldo P. Franca
author: T. J. R. Hughes
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1987-01-01T00:00:00Z
review text: The arch problem with shear deformation based upon the Hellinger-Reissner variational formulation is studied in a parameter-dependent form. A mixed Petrov-Galerkin method is used to construct a discrete approximation. Finite elements with equal-order discontinuous stress and continuous displacement interpolations, unstable in the Galerkin method, are proved to be stable in the new formulation. Error estimates indicate optimal rates of convergence for displacements and suboptimal rates, with gap one, for stresses. Numerical experiments confirm these estimates. The good accuracy of the mixed Petrov-Galerkin method is illustrated in some deep and shallow thin arch examples. No shear or membrane locking is present using full integration schemes.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 3982681
zbMATH Keywords: arch problem
zbMATH Keywords: shear deformation
zbMATH Keywords: Hellinger-Reissner variational formulation
zbMATH Keywords: parameter-dependent form
zbMATH Keywords: mixed Petrov-Galerkin method
zbMATH Keywords: discrete approximation
zbMATH Keywords: elements with equal-order discontinuous stress
zbMATH Keywords: continuous displacement interpolations
zbMATH Keywords: stable
zbMATH Keywords: error estimates
zbMATH Keywords: optimal rates of convergence for displacements
zbMATH Keywords: suboptimal rates, with gap one, for stresses
MaRDI profile type: Publication
full work available at URL: 0045-7825(87)90074-0
OpenAlex ID: W2055767533
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description: scientific article; zbMATH DE number 3982681