Abstract
In finite element simulation of engineering applications, accuracy is of great importance considering that generally no analytical solution is available. Conventional error estimation methods aim to estimate the error in energy norms or the global L2-norm. These values can be used to estimate the accuracy of the model or to guide how to adapt the model to achieve more accuracy. However, in engineering applications specific quantities are required to be accurate. The novel error estimation approach which is called Dual-Weighted Residual (DWR) error estimation, approximates the error with respect to the quantity of interest which can be mean stress or displacement in a subspace or the solution ('s gradient) on a specific point, etc. DWR error estimation is a dual-based scheme which requires an adjoint (dual) problem. The dual problem is described by defining the quantity of interest in a functional form. Then by solving the primal and dual problems, errors in terms of the specified quantities are calculated. In this paper the DWR error estimation besides the conventional residual-based error estimation and a recovery-based error estimation are applied in a three-dimensional elasticity problem. Local estimated errors are exploited in order to accomplish the mesh adaptivity procedure. The goal-oriented mesh adaptivity control the local errors in terms of the prescribed quantities. Both refinement and coarsening processes are applied to raise the efficiency. The convergence rates are plotted to illustrate the superiorities of the goal-oriented adaptivity over the traditional ones.
| Original language | English |
|---|---|
| Title of host publication | 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 |
| Publisher | International Center for Numerical Methods in Engineering |
| Pages | 734-745 |
| Number of pages | 12 |
| ISBN (Print) | 9788494284472 |
| Publication status | Published - 2014 Jul 1 |
| Event | Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014 - Barcelona, Spain Duration: 2014 Jul 20 → 2014 Jul 25 |
Other
| Other | Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014 |
|---|---|
| Country | Spain |
| City | Barcelona |
| Period | 14/7/20 → 14/7/25 |
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Keywords
- Convergence rate
- Dual-Weighted Residual
- Goal-oriented error estimation
- Linear quantity of interest
- Local mesh adaptivity
ASJC Scopus subject areas
- Mechanics of Materials
- Computational Theory and Mathematics
- Computer Science Applications
- Mechanical Engineering
Cite this
Goal-oriented error estimation and mesh adaptivity in three-dimentional elasticity problems. / Ghorashi, S. Sh; Amani, J.; Bagherzadeh, A. S.; Rabczuk, Timon.
11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014. International Center for Numerical Methods in Engineering, 2014. p. 734-745.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Goal-oriented error estimation and mesh adaptivity in three-dimentional elasticity problems
AU - Ghorashi, S. Sh
AU - Amani, J.
AU - Bagherzadeh, A. S.
AU - Rabczuk, Timon
PY - 2014/7/1
Y1 - 2014/7/1
N2 - In finite element simulation of engineering applications, accuracy is of great importance considering that generally no analytical solution is available. Conventional error estimation methods aim to estimate the error in energy norms or the global L2-norm. These values can be used to estimate the accuracy of the model or to guide how to adapt the model to achieve more accuracy. However, in engineering applications specific quantities are required to be accurate. The novel error estimation approach which is called Dual-Weighted Residual (DWR) error estimation, approximates the error with respect to the quantity of interest which can be mean stress or displacement in a subspace or the solution ('s gradient) on a specific point, etc. DWR error estimation is a dual-based scheme which requires an adjoint (dual) problem. The dual problem is described by defining the quantity of interest in a functional form. Then by solving the primal and dual problems, errors in terms of the specified quantities are calculated. In this paper the DWR error estimation besides the conventional residual-based error estimation and a recovery-based error estimation are applied in a three-dimensional elasticity problem. Local estimated errors are exploited in order to accomplish the mesh adaptivity procedure. The goal-oriented mesh adaptivity control the local errors in terms of the prescribed quantities. Both refinement and coarsening processes are applied to raise the efficiency. The convergence rates are plotted to illustrate the superiorities of the goal-oriented adaptivity over the traditional ones.
AB - In finite element simulation of engineering applications, accuracy is of great importance considering that generally no analytical solution is available. Conventional error estimation methods aim to estimate the error in energy norms or the global L2-norm. These values can be used to estimate the accuracy of the model or to guide how to adapt the model to achieve more accuracy. However, in engineering applications specific quantities are required to be accurate. The novel error estimation approach which is called Dual-Weighted Residual (DWR) error estimation, approximates the error with respect to the quantity of interest which can be mean stress or displacement in a subspace or the solution ('s gradient) on a specific point, etc. DWR error estimation is a dual-based scheme which requires an adjoint (dual) problem. The dual problem is described by defining the quantity of interest in a functional form. Then by solving the primal and dual problems, errors in terms of the specified quantities are calculated. In this paper the DWR error estimation besides the conventional residual-based error estimation and a recovery-based error estimation are applied in a three-dimensional elasticity problem. Local estimated errors are exploited in order to accomplish the mesh adaptivity procedure. The goal-oriented mesh adaptivity control the local errors in terms of the prescribed quantities. Both refinement and coarsening processes are applied to raise the efficiency. The convergence rates are plotted to illustrate the superiorities of the goal-oriented adaptivity over the traditional ones.
KW - Convergence rate
KW - Dual-Weighted Residual
KW - Goal-oriented error estimation
KW - Linear quantity of interest
KW - Local mesh adaptivity
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UR - http://www.scopus.com/inward/citedby.url?scp=84923950795&partnerID=8YFLogxK
M3 - Conference contribution
SN - 9788494284472
SP - 734
EP - 745
BT - 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014
PB - International Center for Numerical Methods in Engineering
ER -