A Refined Error Analysis of (original) (raw)
Related papers
On Mixed Finite Element Methods for the Reissner-Mindlin Plate Model
Mathematics of Computation, 1992
In this paper we analyze the convergence of mixed finite element approximations to the solution of the Reissner-Mindlin plate problem. We show that several known elements fall into our analysis, thus providing a unified approach. We also introduce a low-order triangular element which is optimalorder convergent uniformly in the plate thickness.
Residual-based a posteriori error estimate for a mixed Reißner-Mindlin plate finite element method
Numerische Mathematik, 2006
Reliable and efficient residual-based a posteriori error estimates are established for the stabilised locking-free finite element methods for the Reissner-Mindlin plate model. The error is estimated by a computable error estimator from above and below up to multiplicative constants that do neither depend on the mesh-size nor on the plate's thickness and are uniform for a wide range of stabilisation parameter. The error is controlled in norms that are known to converge to zero in a quasi-optimal way. An adaptive algorithm is suggested and run for improving the convergence rates in three numerical examples for thicknesses 0.1, .001 and .001.
Mixed-interpolated elements for Reissner-Mindlin plates
International Journal for Numerical Methods in Engineering, 1989
We present in this paper a procedure to establish Reissner-Mindlin plate bending elements. The procedure is based on the idea to combine known resuits on the approximation of Stokes problems with known results on the approximation of elliptic problems. The proposed elements satisfy the mathematical conditions of stability and convergence, and some of them promise to provide efficient elements for practical solutions. *The abbreviation MITC4 is used to designate our clement based on 'mixed interpolated tensorial components with four nodes' and we use similar abbrcviations for the other elements we introduce
Analysis of a Linear–Linear Finite Element for the Reissner–Mindlin Plate Model
Mathematical Models and Methods in Applied Sciences, 1997
An analysis is presented for a recently proposed nite element method for the Reissner{ Mindlin plate problem. The method is based on the standard variational principle, uses nonconforming linear elements to approximate the rotations and conforming linear elements to approximate the transverse displacements, and avoids the usual \locking problem" by interpolating the shear stress into a rotated space of lowest order Raviart-Thomas elements. When the plate thickness t = O(h), it is proved that the method gives optimal order error estimates uniform in t. However, the analysis suggests and numerical calculations con rm that the method can produce poor approximations for moderate sized values of the plate thickness. Indeed, for t xed, the method does not converge as the mesh size h tends to zero.
A Refined Error Analysis of Mitc Plate Elements
Mathematical Models and Methods in Applied Sciences, 2006
We consider the Mixed Interpolated (Tensorial Components) finite element families for the Reissner–Mindlin plate model. For the case of a convex domain with clamped boundary conditions, we prove regularity results and derive new error estimates which are uniformly valid with respect to the thickness parameter.
Guaranteed Functional Error Estimates for the Reissner-Mindlin Plate Problem
Journal of Mathematical Sciences, 2006
We consider a class of explicitly computed majorants that provide accuracy estimates for a solution to the Reissner-Mindlin plate problem. The proof is based on a generalized statement of the problem. It does not require any extra analysis of properties of controlled approximate solutions is independent of features of the finite element method for obtaining approximate solutions. Bibliography: 13 titles. Illustrations: 1
Error estimates for low-order isoparametric quadrilateral finite elements for plates
This paper deals with the numerical approximation of the bending of a plate modeled by Reissner-Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is based on the family of elements called MITC (mixed interpolation of tensorial components). We consider two lowest-order methods of this family on quadrilateral meshes.
On the uniform approximation of the Reissner-Mindlin plate model by p/hp finite element methods
Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), 2002
We study the approximation of the Reissner-Mindlin plate using the p/hp version of the finite element method (FEM). Our goal is to identify a method that: (i) is free of shear locking, (ii) approximates the boundary layer independently of the thickness of the plate and (iii) converges exponentially with respect to the number of degrees of freedom. We will consider both standard and reduced constraint/mixed formulations, in the context of the p/hp version of the FEM, and we will give guidelines for the construction of appropriate mesh-degree combinations that accomplish the above three goals, using straight as well as curved sided elements.
Analysis of a mixed finite element method for the Reissner-Mindlin plate problems
Computer Methods in Applied Mechanics and Engineering, 1998
An analysis of a triangular mixed finite element method, proposed by Taylor and Auricchio [13] is presented. The method is based on a linked interpolation between deflections and rotations in order to avoid the locking phenomenon (cf. ). The analysis shows that the approximated deflections and rotations are first order convergent to the exact solution, uniformly in the thickness.
Mathematics of Computation, 1999
We consider mixed finite element discretizations of linear second order elliptic boundary value problems with respect to an adaptively generated hierarchy of possibly highly nonuniform simplicial triangulations. In particular, we present and analyze four different kinds of error estimators: a residual based estimator, a hierarchical one, error estimators relying on the solution of local subproblems and on a superconvergence result, respectively. Finally, we examine the relationship between the presented error estimators and compare their local components.