The HP-MITC finite element method for the Reissner-Mindlin Plate Problem

M. Ainsworth, K. Pinchedez

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The popular MITC finite elements used for the approximation of the Reissner-Mindlin plate are extended to the case where elements of non-uniform degree p distribution are used on locally refined meshes. Such an extension is of particular interest to the hp-version and hp-adaptive finite element methods. A priori error bounds are provided showing that the method is locking-free. The analysis is based on new approximation theoretic results for non-uniform Brezzi-Douglas-Fortin-Marini spaces, and extends the results obtained in the case of uniform order approximation on globally quasi-uniform meshes presented by Stenberg and Suri (SIAM J. Numer. Anal. 34 (1997) 544). Numerical examples illustrating the theoretical results and comparing the performance with alternative standard Galerkin approaches are presented for two new benchmark problems with known analytic solution, including the case where the shear stress exhibits a boundary layer. The new method is observed to be locking-free and able to provide exponential rates of convergence even in the presence of boundary layers.
Original languageEnglish
Pages (from-to)429-462
Number of pages33
JournalJournal of Computational and Applied Mathematics
Volume148
Issue number2
DOIs
Publication statusPublished - 2002

Fingerprint

Hp Finite Elements
Mindlin plates
Reissner-Mindlin Plate
Locking-free
Boundary layers
Finite Element Method
Finite element method
Boundary Layer
Mesh
A Priori Error Bounds
Hp-version
Shear stress
Adaptive Finite Element Method
Approximation Order
Approximation
Shear Stress
Analytic Solution
Galerkin
Rate of Convergence
Benchmark

Keywords

  • Reissner-Mindlin
  • applied mathematics
  • HP-MITC
  • numerical analysis

Cite this

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The HP-MITC finite element method for the Reissner-Mindlin Plate Problem. / Ainsworth, M.; Pinchedez, K.

In: Journal of Computational and Applied Mathematics, Vol. 148, No. 2, 2002, p. 429-462.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Ainsworth, M.

AU - Pinchedez, K.

PY - 2002

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AB - The popular MITC finite elements used for the approximation of the Reissner-Mindlin plate are extended to the case where elements of non-uniform degree p distribution are used on locally refined meshes. Such an extension is of particular interest to the hp-version and hp-adaptive finite element methods. A priori error bounds are provided showing that the method is locking-free. The analysis is based on new approximation theoretic results for non-uniform Brezzi-Douglas-Fortin-Marini spaces, and extends the results obtained in the case of uniform order approximation on globally quasi-uniform meshes presented by Stenberg and Suri (SIAM J. Numer. Anal. 34 (1997) 544). Numerical examples illustrating the theoretical results and comparing the performance with alternative standard Galerkin approaches are presented for two new benchmark problems with known analytic solution, including the case where the shear stress exhibits a boundary layer. The new method is observed to be locking-free and able to provide exponential rates of convergence even in the presence of boundary layers.

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