Guaranteed error bounds on pointwise quantities of interest for transient viscodynamics problems

Waeytens, Julien; Chamoin, Ludovic

doi:10.1007/s00466-011-0642-1

Cited by 28 publications

(38 citation statements)

References 35 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%

“…For instance, the parallelogram identity is used in [7,65,66] in the context of linear elasticity and in [21,22] for transient convection-diffusion-reaction equations. In the framework of structural dynamics reference [46] proposes a bounding expression, alternative to the one in equation (76) originally proposed in reference [45].…”

Section: Bounds Using Symmetric Error Equationsmentioning

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%

“…The elementary contributions η s n,k are computed restricting the integrals in equation (45) to the elements Ω k . The numerical methodology providing v * n and σ * n is detailed below.…”

Section: Assessing Space Discretization Errorsmentioning

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%

See 4 more Smart Citations

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: Bounds Using Symmetric Error Equationsmentioning

confidence: 99%

Section: The Estimation Of Value Lmentioning

confidence: 99%

Section: Assessing Space Discretization Errorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Error Assessment in Structural Transient Dynamics

Verdugo

Mariné

Dı́ez

2014

Arch Computat Methods Eng

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Modal‐based goal‐oriented error assessment for timeline‐dependent quantities in transient dynamics

Verdugo

Mariné

Dı́ez

2013

Numerical Meth Engineering

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This article presents a new approach to assess the error in specific quantities of interest in the framework of linear elastodynamics. In particular, a new type of quantities of interest (referred as timeline-dependent quantities) is proposed. These quantities are scalar time-dependent outputs of the transient solution, which are better suited to time-dependent problems than the standard scalar ones, frozen in time. The proposed both the standard scalar and the new timeline-dependent quantities of interest. The key ingredient is the modal-based approximation of the associated adjoint problems, which allows efficiently computing and storing the adjoint solution.\ud The approximated adjoint solution is readily post-processed to produce an enhanced solution, requiring only one spatial post-process for each vibration mode and using the time-harmonic hypothesis to recover\ud the time dependence. Thus, the proposed goal-oriented error estimate consists in injecting this enhanced adjoint solution into the residual of the direct problem. The resulting estimate is very well suited for transient dynamic simulations because the enhanced adjoint solution is computed before starting the forward time integration of the direct problem. Thus, the cost of the error estimate at each time step is very low.Peer ReviewedPostprint (published version

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Goal‐oriented adaptivity using unconventional error representations for the multidimensional Helmholtz equation

Darrigrand

Rodríguez-Rozas

Muga

et al. 2017

Numerical Meth Engineering

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SummaryIn goal-oriented adaptivity, the error in the quantity of interest is represented using the error functions of the direct and adjoint problems. This error representation is subsequently bounded above by element-wise error indicators that are used to drive optimal refinements. In this work, we propose to replace, in the error representation, the adjoint problem by an alternative operator. The main advantage of the proposed approach is that, when judiciously selecting such alternative operator, the corresponding upper bound of the error representation becomes sharper, leading to a more efficient goal-oriented adaptivity.While the method can be applied to a variety of problems, we focus here on two-and three-dimensional (2-D and 3-D) Helmholtz problems. We show via extensive numerical experimentation that the upper bounds provided by the alternative error representations are sharper than the classical ones and lead to a more robust p-adaptive process. We also provide guidelines for finding operators delivering sharp error representation upper bounds. We further extend the results to a convection-dominated diffusion problem as well as to problems with discontinuous material coefficients. Finally, we consider a sonic logging-while-drilling problem to illustrate the applicability of the proposed method.

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Guaranteed error bounds on pointwise quantities of interest for transient viscodynamics problems

Cited by 28 publications

References 35 publications

Error Assessment in Structural Transient Dynamics

Error Assessment in Structural Transient Dynamics

Modal‐based goal‐oriented error assessment for timeline‐dependent quantities in transient dynamics

Goal‐oriented adaptivity using unconventional error representations for the multidimensional Helmholtz equation

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