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See detailLocally equilibrated stress recovery for goal oriented error estimation in the extended finite element method
Bordas, Stéphane UL; gonzález-estrada, octavio andrés; ródenas, Juan josé et al

in Computers & Structures (2015)

Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of finite element numerical simulations that involve complex domains. By locally improving ... [more ▼]

Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of finite element numerical simulations that involve complex domains. By locally improving the approximation qual- ity, for example, by using the extended finite element method (XFEM), we can solve expensive problems which could result intractable otherwise. Here, we present an error estimation technique for enriched finite element approxi- mations that is based on an equilibrated recovery technique, which considers the stress intensity factor as the quantity of interest. The locally equilibrated superconvergent patch recovery is used to obtain enhanced stress fields for the primal and dual problems defined to evaluate the error estimate. [less ▲]

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See detailMesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery
González-Estrada, O. A.; Nadal, E.; Ródenas, J. J. et al

in Computational Mechanics (2013)

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for ... [more ▼]

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for design purposes (e.g. the mean stress or mean displacement in a particular area, the stress intensity factor for fracture problems). These GOEE are one of the key unsolved problems of advanced engineering applications in, for example, the aerospace industry. This work presents a simple recovery-based error estimation technique for QoIs whose main characteristic is the use of an enhanced version of the Superconvergent Patch Recovery (SPR) technique previously used for error estimation in the energy norm. This enhanced SPR technique is used to recover both the primal and dual solutions. It provides a nearly statically admissible stress field that results in accurate estimations of the local contributions to the discretisation error in the QoI and, therefore, in an accurate estimation of this magnitude. This approach leads to a technique with a reasonable computational cost that could easily be implemented into already available finite element codes, or as an independent postprocessing tool. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

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See detailExplicit expressions of dual loads for accurate error estimation and bounding in goal oriented adaptivity
Ródenas, Juan José; Nadal, Enrique; González-Estrada, Octavio Andrés et al

in Moitinho de Almeida, J P; Díez, P; Tiago, C (Eds.) et al Adaptive Modeling and Simulation. Proceedings of VI ADMOS 2013 (2013)

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See detailAccurate error estimate in energy norm using a nearly-equilibrated kinematically-admissible displacement recovery technique
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in Pimienta, P M (Ed.) 10th World Congress on Computational Mechanics (WCCM 2012) (2012)

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See detailPractical error bounds in energy norm based on a recovered displacement field
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in Pimienta, P M (Ed.) 10th World Congress on Computational Mechanics (WCCM 2012) (2012)

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See detailError estimation and error bounding in energy norm based on a displacement recovery technique
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers (2012)

Traditionally, recovery based error estimators in linear elasticity have considered the evaluation of an enhanced stress field obtained from the raw Finite Element (FE) stress solution. Instead of that ... [more ▼]

Traditionally, recovery based error estimators in linear elasticity have considered the evaluation of an enhanced stress field obtained from the raw Finite Element (FE) stress solution. Instead of that, one can also obtain a recovered displacement field from the FE displacements. Herein, we describe a superconvergent patch recovery of the displacement field which considers the local fulfilment of boundary and internal equilibrium equations, Dirichlet constraints and, for singular problems, the splitting of the displacement and stress fields into singular and smooth parts. Numerical tests using problems with known analytical solution have been carried out to validate the proposed technique for error estimation and error bounding in energy norm and quantities of interest. [less ▲]

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See detailError estimation and bounding in energy norm based on a displacement recovery technique
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in Eberhardsteiner, Josef; Böhm, Helmut; Rammerstorfer, F G (Eds.) 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) (2012)

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See detailError estimation of recovered solutions in FE analysis. Higher order h-adaptive refinement strategies
Ródenas, J. J.; Nadal, E.; González-Estrada, O. A. et al

in Pimienta, P M (Ed.) 10th World Congress on Computational Mechanics (WCCM 2012) (2012)

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See detailError estimation and error bounding in quantities of interest based on equilibrated recovered displacement fields
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers (2012)

Over the last ten years there has been an increase on the use of goal-oriented error estimates aimed to quantify the local error on a (non)linear quantity of interest (QoI) that might result relevant for ... [more ▼]

Over the last ten years there has been an increase on the use of goal-oriented error estimates aimed to quantify the local error on a (non)linear quantity of interest (QoI) that might result relevant for design purposes. Residual-based error estimators have been used recursively to obtain upper and lower bounds of the error in quantities of interest for finite element approximations. In this paper, we present a recovery technique for 2D linear elasticity problems, based on the superconvergent patch recovery (SPR), which provides recovered displacement and stress fields that are then utilised to evaluate practical upper and lower error bounds in QoI. [less ▲]

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See detailOn the use of recovery techniques for accurate error estimation and error bounding in XFEM
Ródenas, J. J.; González-Estrada, O. A.; Fuenmayor, F. J. et al

in Bordas, Stéphane; Kerfriden, Pierre (Eds.) 2nd International Conference on the Extended Finite Element Method (2011)

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See detailComparison of recently developed recovery type discretization error estimators for the extended finite element method
Ródenas, J. J.; Duflot, Marc; Bordas, Stéphane UL et al

in Schrefler, B A; Perego, U (Eds.) 8th World Congress on Computational Mechanics (WCCM8). 5th.European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) (2008)

Detailed reference viewed: 61 (1 UL)