Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery

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 ▲]

Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

in Computational Mechanics (2013), 52(1), 37-52

An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown ... [more ▼]

An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a "smooth + singular" decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features. © 2012 Springer-Verlag. [less ▲]

Equilibrated patch recovery for accurate evaluation of upper error bounds in quantities of interest

in ECCOMAS Thematic Conference - ADMOS 2011: International Conference on Adaptive Modeling and Simulation, An IACM Special Interest Conference (2012)

There is an increasing interest on the use of goal-oriented error estimates which help to measure and control the local error on a linear or non-linear quantity of interest (QoI) that might result ... [more ▼]

There is an increasing interest on the use of goal-oriented error estimates which help to measure and control the local error on a linear or non-linear quantity of interest (QoI) that might result relevant for design purposes (e.g. the mean stress value in a particular area, displacements, the stress intensity factor for fracture problems,⋯). In general, residual-based error estimators have been used to obtain upper and lower bounds of the error in quantities of interest for finite element approximations. In this work, we propose a novel a posteriori recovery technique to obtain an upper error bound of the QoI. We use a recovery procedure based on the superconvergent patch recovery (SPR) technique to obtain nearly statically admissible recovered stress fields for the primal and dual problems. This recovery technique was previously used to obtain upper bounds of the error in energy norm and has been used in this paper to obtain a computable version of the upper bound for the quantity of interest. [less ▲]

Error estimation and error bounding in energy norm based on a displacement recovery technique

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 ▲]

Error estimation in quantities of interest for XFEM using recovery techniques

in Yang, Z J (Ed.) 20th UK National Conference of the Association for Computational Mechanics in Engineering (ACME) (2012)

Error estimation and error bounding in quantities of interest based on equilibrated recovered displacement fields

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 ▲]

Equilibrated patch recovery for accurate evaluation of upper error bounds in quantities of interest

in Audry, D; Díez, P; Tie, B (Eds.) et al Adaptive Modeling and Simulation. Proceedings of V ADMOS 2011 (2011)

Accurate evaluation of stress intensity factors using error estimation in quantities of interest based on equilibrated recovery

in Oliver, J; Jirasek, M; Allix, O (Eds.) et al Computational Modeling of Fracture and Failure of Materials and Structures. Proceedings of CFRAC 2011 (2011)

During the last years the use of error estimators which measure the error in a quantity of interest defined by the analyst, instead of the energy norm, have become increasingly popular as they provide an ... [more ▼]

During the last years the use of error estimators which measure the error in a quantity of interest defined by the analyst, instead of the energy norm, have become increasingly popular as they provide an error indicator for goal oriented adaptivity procedures. In this paper we propose an a posteriori recovery-based error estimation procedure which considers the stress intensity factor K typical of singular problems as the quantity of interest in finite element (FE) approximations. In general, error estimators in quantities of interest have been based on residual techniques and, although recovery techniques have been often preferred when considering the error in energy norm due to their robustness and simplicity, so far, there is no available procedure which considers an equilibrated recovery technique that can be used in standard FE frameworks. In [1] a standard SPR recovery technique is used to obtain an error measure of the J-integral, which is closely related to the value of the SIF. However, it does not consider any equilibrium constraints or the singularity near the crack tip, thus the obtained recovered stress field is not well suited for this kind of problems. The technique proposed herein relies on the enhanced superconvergent patch recovery technique presented in [2] to evaluate highly accurate recovered stress fields of the primal and dual problems, which are then used to obtain a sharp error estimate. The primal problem is simply the problem under analysis. To formulate the dual problem we consider the linear interaction integral representing K to obtain the applied loads of the dual FE approximation to solve. The high accuracy of the recovered stress fields for both the primal and dual solutions is obtained by decomposing the raw stress field obtained from the finite element approximations into singular and smooth parts, and enforcing the fulfilment of boundary and internal equilibrium equations. The results indicate an accurate estimation of the error in K for benchmark problems with exact solution. [less ▲]

On the use of recovery techniques for accurate error estimation and error bounding in XFEM

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

Comparison of recently developed recovery type discretization error estimators for the extended finite element method

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)