Journal ArticleDOI
Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements
TLDR
The upper and lower bounds for the effectivity index on the a posteriori estimate of the error in the finite element method are given explicitly for a certain concrete estimator for linear elements as mentioned in this paper.Abstract:
This paper adresses the problem of determining upper and lower bounds for the effectivity index on the a posteriori estimate of the error in the finite element method. These bounds are given explicitly for a certain concrete estimator for linear elements and unstructured triangular meshes. They depend strongly on the geometry of the triangles and (relatively weakly) on the smoothness of the solution. An example shows that the bounds are not over pessimistic. In Babuska, Plank, and Rodriguez (4) detailed numerical experimentation is given.read more
Citations
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Book
A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques
TL;DR: Introduction.
Journal ArticleDOI
A posteriori error estimation and adaptive mesh-refinement techniques
TL;DR: In this paper, three different a posteriori error estimators for elliptic partial differential equations are analyzed and three different mesh-refinement techniques based on these estimators are capable to detect local singularities of the solution and to appropriately refine the grid near these singularities.
Journal ArticleDOI
Validation of A-Posteriori Error Estimators by Numerical Approach
TL;DR: In this article, a numerical methodology which determines the quality (or robustness) of a-posteriori error estimators for finite-element solutions of linear elliptic problems is described.
Journal ArticleDOI
Local and parallel finite element algorithms based on two-grid discretizations
Jinchao Xu,Aihui Zhou +1 more
TL;DR: A number of new local and parallel discretization and adaptive nite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems and the main idea is to use a coarse grid to approximate the low frequencies and then to correct the resulted residue (which contains mostly high frequencies) by some local/parallel procedures.
Journal ArticleDOI
A Local Regularization Operator for Triangular and Quadrilateral Finite Elements
C. Bernardi,V. Girault +1 more
TL;DR: A local regularization operator on triangular or quadrilateral finite elements built on structured or unstructured meshes is developed and it is proved that it has the same optimal approximation properties as the standard interpolation operator.
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.
Journal ArticleDOI
Les inéquations en mécanique et en physique
Journal ArticleDOI
Error Estimates for Adaptive Finite Element Computations
I. Babuvška,W. C. Rheinboldt +1 more
TL;DR: The main theorem gives an error estimate in terms of localized quantities which can be computed approximately, and the estimate is optimal in the sense that, up to multiplicative constants which are independent of the mesh and solution, the upper and lower error bounds are the same.
Journal ArticleDOI
Some a posteriori error estimators for elliptic partial differential equations
Randolph E. Bank,A. Weiser +1 more
TL;DR: Three new a posteriori error estimators in the energy norm for finite element solutions to elliptic partial differential equations are presented and it is proved that as the mesh size decreases, under suitable assumptions, two of the error estimator approach upper bounds on the norm of the true error.
Journal ArticleDOI
The $h-p$ version of the finite element method with quasiuniform meshes
Ivo Babuška,Manil Suri +1 more
TL;DR: In this paper, the classical error estimates for the h-version of the finite element method are extended for the H-p version, expressed as explicit functions of h and p. The estimates are given for the case where the solution u (H sub k) has singularities at the corners of the domain.
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Some a posteriori error estimators for elliptic partial differential equations
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