Journal ArticleDOI
The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
O. C. Zienkiewicz,J. Z. Zhu +1 more
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In this article, a general recovery technique is developed for determining the derivatives (stresses) of the finite element solutions at nodes, which has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems.Abstract:
This is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation. In this paper, a general recovery technique is developed for determining the derivatives (stresses) of the finite element solutions at nodes. The implementation of the recovery technique is simple and cost effective. The technique has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems. Numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent. One order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements. In particular, an O(h4) convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time. The performance of the proposed technique is compared with the widely used smoothing procedure of global L2 projection and other methods. It is found that the derivatives recovered at interelement nodes, by using L2 projection, are also superconvergent for linear elements but not for quadratic elements. Numerical experiments on the convergence of the recovered solutions in the energy norm are also presented. Higher rates of convergence are again observed. The results presented in this part of the paper indicate clearly that a new, powerful and economical process is now available which should supersede the currently used post-processing procedures applied in most codes.read more
Citations
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Journal ArticleDOI
Numerical analysis of strain localization in metal powder‐forming processes
Roland W. Lewis,Amir R. Khoei +1 more
TL;DR: In this paper, a method is presented for applying the mixed formulation to study the prediction of localization phenomenon in powder-forming processes and an adaptive analysis using element elongation is applied in the modelling of strain localization.
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Goal-oriented error estimation and adaptive mesh refinement in dynamic coupled thermoelasticity
TL;DR: AMR for dynamic coupled thermoelasticity problems based on GOEE is presented and WSPR predicts the error more accurate and effective than SPR and L 2 -PR methods.
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A NURBS-based generalized finite element scheme for 3D simulation of heterogeneous materials
TL;DR: 3D NURBS-based interface-enriched generalized finite element method (NIGFEM) is introduced to solve problems with complex discontinuous gradient fields observed in the analysis of heterogeneous materials and provides additional advantages including the accurate capture of the solution fields in the vicinity of material interfaces and the built-in capability for hierarchical mesh refinement.
Proceedings ArticleDOI
A general continuous sensitivity equation formulation for complex flows
TL;DR: In this article, a general formulation of the continuous sensitivity equation method was developed to account for a complex parameter dependence in both flow variables and physical fluid properties (such as viscosity, thermal conductivity, etc.).
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Polygonal type variable-node elements by means of the smoothed finite element method for analysis of two-dimensional fluid-solid interaction problems in viscous incompressible flows
Jungdo Kim,Seyoung Im +1 more
TL;DR: By using polygonal elements, a seamless connection is achieved between non-matching meshes satisfying the interface conditions of continuity and compatibility, and the smoothed finite element methods yielded better accuracy compared with the conventional FEM.
References
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Journal ArticleDOI
A simple error estimator and adaptive procedure for practical engineerng analysis
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes.
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Local and global smoothing of discontinuous finite element functions using a least squares method
E. Hinton,John S. Campbell +1 more
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Optimal stress locations in finite element models
TL;DR: In this paper, the existence of optimal points for calculating accurate stresses within finite element models is discussed and a method for locating such points is proposed and applied to several popular finite elements.
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The post-processing approach in the finite element method—part 1: Calculation of displacements, stresses and other higher derivatives of the displacements
Ivo Babuška,A. Miller +1 more
TL;DR: In this article, a method for post-processing a finite element solution to obtain high accuracy approximations for displacements, stresses, stress intensity factors, etc. is presented.
Journal ArticleDOI
Higher order local accuracy by averaging in the finite element method
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TL;DR: In this paper, the authors describe the class of finite element subspaces and explain the main result on the accuracy of K h * u h, where K h is a fixed function, u h represents local averages, and * denotes convolution.
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