Guaranteed computable bounds on quantities of interest in finite element computations

M. Ainsworth, R. Rankin

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1605-1634
Number of pages30
JournalInternational Journal for Numerical Methods in Engineering
Issue number13
Publication statusPublished - 2012


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


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