Journal Article10.1016/S0045-7949(98)00235-1
Adaptive h-version eigenfrequency analysis
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TL;DR: An adaptive h-version finite element scheme to control the discretization error in free vibration analysis is presented and the nice properties of the final local and global updated solution are shown as a basis for an error estimator and an error indicator in an adaptive process.
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About: This article is published in Computers & Structures. The article was published on 01 Jun 1999. The article focuses on the topics: Superconvergence & Rate of convergence.
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Citations
Damage detection in bridges using accurate modal parameters
Anjan Dutta,Sudip Talukdar +1 more
TL;DR: In this article, eigenvalue analysis is carried out using Lanczos algorithm in an adaptive h-version finite element environment in order to control the discretization error for accurate evaluation of modal parameters.
119
Patch recovery based on superconvergent derivatives and equilibrium
Nils-Erik Wiberg,Abdulwahab Fehti +1 more
- 01 Jan 1992
TL;DR: In this article, a postprocessing technique is developed for determining first-order derivatives (fluxes, stresses) at nodal points based on derivatives in superconvergent points.
98
Explicit A Posteriori Error Estimates for Eigenvalue Analysis of Heterogeneous Elastic Structures
TL;DR: In this article, an a posteriori error estimator for the eigenvalue analysis of heterogeneous elastic structures was developed for the Eigenvalue Analysis of Heterogeneous Elastic Structures.
31
Adaptive finite element analysis for damage detection of non-uniform Euler–Bernoulli beams with multiple cracks based on natural frequencies
TL;DR: Numerical results are presented for free vibration problems and damage detection problems of representative non-uniform and geometrically stepped Euler–Bernoulli beams with multiple cracks to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method.
Error estimates and adaptive finite element methods: A bibliography (1990‐2000)
TL;DR: Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view.
27
References
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Klaus-Jürgen Bathe,H. Saunders +1 more
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5.6K
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The Symmetric Eigenvalue Problem
Beresford N. Parlett
- 01 Jan 1980
TL;DR: Parlett as discussed by the authors presents mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few.
3.7K
The Symmetric Eigenvalue Problem.
TL;DR: Parlett as discussed by the authors presents mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few.
3.4K
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.
2.5K
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.
2.1K