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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TLDR
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
A superconvergent stress recovery technique for accurate boundary stress extraction
TL;DR: In this article, an element-base superconvergent stress recovery technique is developed for accurate boundary stress extraction, where higher-order stress fields are assumed for all stress components and higher order elements are used for the construction of necessary matrices.
Proceedings ArticleDOI
Super-convergence of Discontinuous Galerkin Method Applied to the Navier-Stokes Equations
TL;DR: It is demonstrated that some flow attributes exhibit super-convergence even in the absence of any post-processing technique, suggesting that flow features that are dominated by global propagation speeds and decay or growth rates should be super- Convergent.
Journal ArticleDOI
Error estimation for the polygonal finite element method for smooth and singular linear elasticity
Octavio Andrés González-Estrada,Sundararajan Natarajan,Juan José Ródenas,Stéphane Bordas,Stéphane Bordas +4 more
TL;DR: A recovery-based error indicator developed to evaluate the quality of polygonal finite element approximations is presented, based on a moving least squares fitting of the finite element stress field.
Journal ArticleDOI
An isogeometrical approach to error estimation and stress recovery
TL;DR: In this article, a new approach for improvement of stresses and estimation of solution errors based on the isogeometrical analysis method is presented, by making use of the superconvergent points, each of the components of the improved tensor is considered as an imaginary surface.
Journal ArticleDOI
Superconvergent second derivative recovery technique and its application in a nonlocal damage mechanics model
Xiaoge Gan,J.E. Akin +1 more
TL;DR: The results show that the proposed technique is capable of evaluating the Laplacian of the equivalent strains and has the potential for even higher order derivative recovery.
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
TL;DR: In this article, the concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced, and the relationship between local smoothing and the reduced integration technique is established.
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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.
Journal ArticleDOI
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
James H. Bramble,A. H. Schatz +1 more
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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