Home  About us  Contact
 

Zhu Error Estimator (zhu + error_estimator)

Distribution by Scientific Domains
Engineering100%

Selected Abstracts

Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz,Zhu error estimator

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2003
M. Picasso
Abstract The framework of Formaggia and Perotto (Numerische Mathematik 2001; 89: 641,667) is considered to derive a new anisotropic error indicator for a Laplace problem in the energy norm. The matrix containing the error gradient is approached using a Zienkiewicz,Zhu error estimator. A numerical study of the effectivity index is proposed for anisotropic unstructured meshes, showing that our indicator is sharp. An anisotropic adaptive algorithm is implemented, aiming at controlling the estimated relative error. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Adaptive superposition of finite element meshes in non-linear transient solid mechanics problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2007
Z. Yue
Abstract An s-adaptive finite element procedure is developed for the transient analysis of 2-D solid mechanics problems with material non-linearity due to progressive damage. The resulting adaptive method simultaneously estimates and controls both the spatial error and temporal error within user-specified tolerances. The spatial error is quantified by the Zienkiewicz,Zhu error estimator and computed via superconvergent patch recovery, while the estimation of temporal error is based on the assumption of a linearly varying third-order time derivatives of the displacement field in conjunction with direct numerical time integration. The distinguishing characteristic of the s-adaptive procedure is the use of finite element mesh superposition (s-refinement) to provide spatial adaptivity. Mesh superposition proves to be particularly advantageous in computationally demanding non-linear transient problems since it is faster, simpler and more efficient than traditional h-refinement schemes. Numerical examples are provided to demonstrate the performance characteristics of the s-adaptive method for quasi-static and transient problems with material non-linearity. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Smart element method I. The Zienkiewicz,Zhu feedback

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2005
Shaofan Li
Abstract A new error control finite element formulation is developed and implemented based on the variational multiscale method, the inclusion theory in homogenization, and the Zienkiewicz,Zhu error estimator. By synthesizing variational multiscale method in computational mechanics, the equivalent eigenstrain principle in micromechanics, and the Zienkiewicz,Zhu error estimator in the finite element method (FEM), the new finite element formulation can automatically detect and subsequently homogenize its own discretization errors in a self-adaptive and a self-adjusting manner. It is the first finite element formulation that combines an optimal feedback mechanism and a precisely defined homogenization procedure to reduce its own discretization errors and hence to control numerical pollutions. The paper focuses on the following two issues: (1) how to combine a multiscale method with the existing finite element error estimate criterion through a feedback mechanism, and (2) convergence study. It has been shown that by combining the proposed variational multiscale homogenization method with the Zienkiewicz,Zhu error estimator a clear improvement can be made on the coarse scale computation. It is also shown that when the finite element mesh is refined, the solution obtained by the variational eigenstrain multiscale method will converge to the exact solution. Copyright © 2004 John Wiley & Sons, Ltd. [source]