The hp-MITC finite element method for the Reissner-Mindlin plate problem

Authors:
Mark Ainsworth;Katia Pinchedez
Affiliations:
Mathematics Department, Strathclyde University, 26 Richmond Street, Glasgow G1 1XH, UK;Mathematics Department, Strathclyde University, 26 Richmond Street, Glasgow G1 1XH, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 13
Cited 3

The h, p and h-p versions of the finite element method in 1 dimension. Part 1. The error analysis of the p-version.

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The h, p and h-p versions of the finite element method in 1 dimension. Part II. The error analysis of the h and h-p versions

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The h, p and h-p versions of the finite element methods in 1 dimension . Part III. The adaptive h-p version.

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A uniformly accurate finite element method for the Reissner-Mindlin plate

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The boundary layer for the reissner-mindlin plate model

SIAM Journal on Mathematical Analysis
Mixed and hybrid finite element methods

Mixed and hybrid finite element methods
Locking effects in the finite element approximation of plate models

Mathematics of Computation
The P and H-P versions of the finite element method, basic principles and properties

SIAM Review
Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model

SIAM Journal on Mathematical Analysis
The p and hp versions of the finite element method for problems with boundary layers

Mathematics of Computation
An hp Error Analysis of MITC Plate Elements

SIAM Journal on Numerical Analysis
Approximation theory for the hp-version finite element method and application to the non-linear Laplacian

Applied Numerical Mathematics
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems

On the effects of using curved elements in the approximation of the Reissner--Mindlin plate by the p version of the finite element method

Applied Numerical Mathematics
The Use of Curved Elements in the Finite Element Approximation of Thin Plates by High Order p and hp Methods

Journal of Scientific Computing
A p-version MITC finite element method for Reissner-Mindlin plates with curved boundaries

Journal of Computational and Applied Mathematics

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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.