Local error estimators for finite element linear analysis

Rougeot, Ph.; Blanchard, Philippe; Moreau, Julien

doi:10.1016/s0045-7825(98)00339-9

Cited by 70 publications

(77 citation statements)

References 10 publications

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“…Some of these error estimators solve two global problems in parallel [10] whereas other post-process the FE solution [11,12,13]. Under this group we can also include the error estimators based on the Constitutive Relation Error (CRE) introduced by Ladevèze and Leguillon [11] and followed by several contributions for many applications, see for example [14,15,16,17]. This technique compares a kinematically admissible stress field with a statically admissible solution obtained by solving local problems, built using the strong prolongation condition.…”

Section: Introductionmentioning

confidence: 99%

A recovery-explicit error estimator in energy norm for linear elasticity

Nadal

Dı́ez

Ródenas

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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Significant research effort has been devoted to produce one-sided error estimates for Finite Element Analyses, in particular to provide upper bounds of the actual error. Typically, this has been achieved using residual-type estimates. One of the most popular and simpler (in terms of implementation) techniques used in commercial codes is the recovery-based error estimator. This technique produces accurate estimations of the exact error but is not designed to naturally produce upper bounds of the error in energy norm. Some attempts to remedy this situation provide bounds depending on unknown constants. Here, a new step towards obtaining error bounds from the recoverybased estimates is proposed. The idea is 1) to use a locally equilibrated recovery technique to obtain an accurate estimation of the exact error, 2) to add an explicit-type error bound of the lack of equilibrium of the recovered stresses in order to guarantee a bound of the actual error and 3) to efficiently and accurately evaluate the constants appearing in the bounding expressions, thus providing asymptotic bounds. The the numerical tests with h-adaptive refinement process show that the bounding property holds even for coarse meshes, providing upper bounds in practical applications.Error bounding, recovery techniques, explicit residual error estimator

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Section: Introductionmentioning

confidence: 99%

A recovery-explicit error estimator in energy norm for linear elasticity

Nadal

Dı́ez

Ródenas

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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“…For over fifteen years, various methods had been introduced to control the numerical quality of specific quantities of interest, such as local stresses, displacement values; they lead to bounds on functional outputs which are relevant information for design purposes in Mechanics [9,10,11,12,13,14,15,16,17,18,19,20,21]. However, among those global/goal-oriented error estimators built from different methods, few lead to guaranteed and relevant bounds, which is a serious drawback in the domain of robust design.…”

Section: Introductionmentioning

confidence: 99%

On the techniques for constructing admissible stress fields in model verification: Performances on engineering examples

Pled

Chamoin

Ladevèze

2011

Numerical Meth Engineering

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SUMMARYRobust global/goal-oriented error estimation is used nowadays to control the approximate finite element solutions obtained from simulation. In the context of Computational Mechanics, the construction of admissible stress fields (i.e. stress tensors which verify the equilibrium equations) is required to set up strict and guaranteed error bounds (using residual based error estimators) and plays an important role in the quality of the error estimates. This work focuses on the different procedures used in the calculation of admissible stress fields, which is a crucial and technically complicated point. The three main techniques that currently exist, called the element equilibration technique (EET), the star-patch equilibration technique (SPET), and the element equilibration + starpatch technique (EESPT), are investigated and compared with respect to three different criteria, namely the quality of associated error estimators, computational cost and easiness of practical implementation into commercial finite element codes.The numerical results which are presented focus on industrial problems; they highlight the main advantages and drawbacks of the different methods and show that the behavior of the three estimators, which have the same convergence rate as the exact global error, is consistent. Two-and three-dimensional experiments have been carried out in order to compare the performance and the computational cost of the three different approaches. The analysis of the results reveals that the SPET is more accurate than EET and EESPT methods, but the corresponding computational cost is higher. Overall, the numerical tests prove the interest of the hybrid method EESPT and show that it is a correct compromise between quality of the error estimate, practical implementation and computational cost. Furthermore, the influence of the cost function involved in the EET and the EESPT is studied in order to optimize the estimators.

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“…As an example, after a displacement finite element analysis, one may construct a statically admissible σ h field, inspired from the displacement analysis, and use the above results. This way is the Ladevèze method [10]. The symmetrical construction, which could be named dual Ladevèze method, relates to the compatibility error [6].…”

Section: The General Dual Analysismentioning

confidence: 99%

Dual Analysis for Finite Element Solutions of Plate Bending

Debongnie¹,

Nguyen²,

Cung³

Civil-Comp Proceedings

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This paper presents the application of the dual analysis concept to plate bending. In this method, a same problem is analyzed parallely by a displacement and an equilibrium model. The energetic distance between these two models is the sum of both global errors and consequently, an upper bound of each of them. After an exposition of the two models, numerical examples are presented, which illustrate the high obtainable accuracy of the method.

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Local error estimators for finite element linear analysis

Cited by 70 publications

References 10 publications

A recovery-explicit error estimator in energy norm for linear elasticity

A recovery-explicit error estimator in energy norm for linear elasticity

On the techniques for constructing admissible stress fields in model verification: Performances on engineering examples

Dual Analysis for Finite Element Solutions of Plate Bending

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