Journal ArticleDOI
A simple error estimator and adaptive procedure for practical engineerng analysis
O. C. Zienkiewicz,J. Z. Zhu +1 more
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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.Abstract:
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.
The estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors. It can thus be combined with a full adaptive process of refinement or, more simply, provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials.
When combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable.
Estimates other than the energy norm have successfully been applied giving, for instance, a predetermined accuracy of stresses.read more
Citations
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Book
A Posteriori Error Estimation in Finite Element Analysis
Mark Ainsworth,J. Tinsley Oden +1 more
TL;DR: In this paper, a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics is presented, focusing on methods for linear elliptic boundary value problems.
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Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
TL;DR: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software.
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Surrogate-based Analysis and Optimization
Nestor V. Queipo,Raphael T. Haftka,Wei Shyy,Tushar Goel,Rajkumar Vaidyanathan,P. Kevin Tucker +5 more
TL;DR: The multi-objective optimal design of a liquid rocket injector is presented to highlight the state of the art and to help guide future efforts.
Journal ArticleDOI
The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: 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.
Journal ArticleDOI
Quantification of uncertainty in computational fluid dynamics
TL;DR: This review covers Verification, Validation, Confirmation and related subjects for computational fluid dynamics (CFD), including error taxonomies, error estimation and banding, convergence rates, surrogate estimators, nonlinear dynamics, and error estimation for grid adaptation vs Quantification of Uncertainty.
References
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Journal ArticleDOI
Adaptive remeshing for compressible flow computations
TL;DR: An adaptive mesh procedure for improving the quality of steady state solutions of the Euler equations in two dimensions is described, implemented in conjunction with a finite element solution algorithm, using linear triangular elements, and an explicit time-stepping scheme.
Journal ArticleDOI
A posteriori error analysis and adaptive processes in the finite element method: Part I—error analysis
TL;DR: It is shown that an extremely high rate of convergence is reached in practical problems using p-convergent methods, and applications to realistic stress analysis and potential problems are presented.
Journal ArticleDOI
The hierarchical concept in finite element analysis
TL;DR: It is shown that it is possible to use the hierarchical concept for finite element shape functions to construct a range of error estimators which compare well with alternatives and are ideally suited for adaptive refinements of analysis.
Journal ArticleDOI
A posteriori error analysis and adaptive processes in the finite element method: Part II—adaptive mesh refinement
TL;DR: It is shown that an extremely high rate of convergence is reached in practical problems using p-convergent methods, and applications to realistic stress analysis and potential problems are presented.
Journal ArticleDOI
Adaptive approaches and reliability estimations in finite element analysis
Ivo Babuška,Werner C. Rheinboldt +1 more
TL;DR: An overview is presented of the authors' recent theoretical and experimental results on reliable and computationally efficient a posteriori error estimates for finite element solutions, and how the results can be extended to the nonlinear case without losing their effectivity.
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The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
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