Model verification in dynamics through strict upper error bounds

Waeytens, Julien

doi:10.1016/j.cma.2008.12.020

Cited by 16 publications

(31 citation statements)

References 13 publications

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“…The same rationale holds for other damped versions of problem (1). For instance, references [44,42,45] introduce damping in the constitutive relation (2) using the linear Maxwell viscous model.…”

Section: Constitutive Relation Error and Implicit Estimatesmentioning

confidence: 99%

“…O (e) requires introducing an auxiliary problem associated with functional L O (·), usually denoted by adjoint or dual problem [31,47,42,43,44,45,46]. The variational form of the adjoint problem consists in finding…”

Section: The Estimation Of Value Lmentioning

confidence: 99%

“…In this context, different estimates provide also indicators driving mesh adaptive procedures, either using energy-like measures [29,30,31,32,33,34] or QoI [35,36,37,38]. Estimates providing error bounds are also available both for energy-like error measures [39,40,41] and goal-oriented ones [42,43,44,45,46,47,31].…”

Section: Introductionmentioning

confidence: 99%

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Error Assessment in Structural Transient Dynamics

Verdugo

Mariné

Dı́ez

2014

Arch Computat Methods Eng

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This paper presents in a unified framework the most representative state-of-the-art techniques on a posteriori error assessment for second order hyperbolic problems, i.e., structural transient dynamics. For the sake of presentation, the error estimates are grouped in four types: recovery-based estimates, the dual weighted residual method, the constitutive relation error method and error estimates for timeline-dependent quantities of interest. All these methodologies give a comprehensive overview on the available error assessment techniques in structural dynamics, both for energy-like and goal-oriented estimates.

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Section: Constitutive Relation Error and Implicit Estimatesmentioning

confidence: 99%

Section: The Estimation Of Value Lmentioning

confidence: 99%

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Error Assessment in Structural Transient Dynamics

Verdugo

Mariné

Dı́ez

2014

Arch Computat Methods Eng

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“…The error estimation tools dealing with transient problems are not so popular, especially in the case of structural dynamics. Some of the contributions on this last topic are, on the one hand, the energy error estimates presented by Aubry et al [8], Li and Wiberg [9,10] and Ladevèze et al [11,12,13,14] and, on the other hand, the goal-oriented estimates proposed by Schleupen and Ramm [15], Fuentes et al [16] and Ladevèze and co-workers [17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

“…The estimates providing bounds have also been extended to transient problems, see for instance [21] where the transient convection-diffusion-reaction equation is considered. To the best knowledge of the authors, the only references discussing bounds in a quantity of interest for linear visco-elastodynamics are due to Ladevèze and co-workers [17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Computable bounds of functional outputs in linear visco-elastodynamics

Verdugo

Dı́ez

2012

Computer Methods in Applied Mechanics and Engineering

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Calculation of strict error bounds for finite element approximations of non‐linear pointwise quantities of interest

Ladevèze

Chamoin

2010

Numerical Meth Engineering

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SUMMARYThis paper deals with the verification of simulations performed using the finite element method. More specifically, it addresses the calculation of strict bounds on the discretization errors affecting pointwise outputs of interest which may be non-linear with respect to the displacement field. The method is based on classical tools, such as the constitutive relation error and extraction techniques associated with the solution of an adjoint problem. However, it uses two specific and innovative techniques: the enrichment of the adjoint solution using a partition of unity method, which enables one to consider truly pointwise quantities of interest, and the decomposition of the non-linear quantities of interest by means of projection properties in order to take into account higher-order terms in establishing the bounds. Thus, no linearization is performed and the property that the local error bounds are guaranteed is preserved. The effectiveness of the approach and the quality of the bounds are illustrated with two-dimensional applications in the context of elastic fatigue problems.

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Model verification in dynamics through strict upper error bounds

Cited by 16 publications

References 13 publications

Error Assessment in Structural Transient Dynamics

Error Assessment in Structural Transient Dynamics

Computable bounds of functional outputs in linear visco-elastodynamics

Calculation of strict error bounds for finite element approximations of non‐linear pointwise quantities of interest

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