### Abstract

Language | English |
---|---|

Pages | 1605-1634 |

Number of pages | 30 |

Journal | International Journal for Numerical Methods in Engineering |

Volume | 89 |

Issue number | 13 |

DOIs | |

State | Published - 2012 |

### Fingerprint

### Keywords

- exact weak solutions
- elasticity
- diffusion-reaction equation
- adaptivity
- a posteriori error estimation
- guaranteed error bounds
- linear functionals

### Cite this

*International Journal for Numerical Methods in Engineering*,

*89*(13), 1605-1634. DOI: 10.1002/nme.3276

}

*International Journal for Numerical Methods in Engineering*, vol. 89, no. 13, pp. 1605-1634. DOI: 10.1002/nme.3276

**Guaranteed computable bounds on quantities of interest in finite element computations.** / Ainsworth, M.; Rankin, R.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Guaranteed computable bounds on quantities of interest in finite element computations

AU - Ainsworth,M.

AU - Rankin,R.

PY - 2012

Y1 - 2012

N2 - We develop and compare a number of alternative approaches to obtain guaranteed and fully computable bounds on the error in quantities of interest of arbitrary order finite element approximations in the context of a linear second-order elliptic problem. In each case, the bounds are fully computable and do not involve any unknown multiplicative factors. Guaranteed computable bounds are also obtained for the case when the Dirichlet boundary conditions are non-homogeneous. This is achieved by taking account of the error incurred by the approximation of the Dirichlet data in the functional used to approximate the quantity of interest itself, which is found to generally give better results. Numerical examples are presented to show that the resulting estimators provide tight bounds with the effectivity index tending to unity from above.

AB - We develop and compare a number of alternative approaches to obtain guaranteed and fully computable bounds on the error in quantities of interest of arbitrary order finite element approximations in the context of a linear second-order elliptic problem. In each case, the bounds are fully computable and do not involve any unknown multiplicative factors. Guaranteed computable bounds are also obtained for the case when the Dirichlet boundary conditions are non-homogeneous. This is achieved by taking account of the error incurred by the approximation of the Dirichlet data in the functional used to approximate the quantity of interest itself, which is found to generally give better results. Numerical examples are presented to show that the resulting estimators provide tight bounds with the effectivity index tending to unity from above.

KW - exact weak solutions

KW - elasticity

KW - diffusion-reaction equation

KW - adaptivity

KW - a posteriori error estimation

KW - guaranteed error bounds

KW - linear functionals

UR - http://www.scopus.com/inward/record.url?scp=84857478230&partnerID=8YFLogxK

U2 - 10.1002/nme.3276

DO - 10.1002/nme.3276

M3 - Article

VL - 89

SP - 1605

EP - 1634

JO - International Journal for Numerical Methods in Engineering

T2 - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 13

ER -