Picture water droplets

Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

Strathprints makes available Open Access scholarly outputs by Strathclyde's Department of Mathematics & Statistics, where continuum mechanics and industrial mathematics is a specialism. Such research seeks to understand fluid dynamics, among many other related areas such as liquid crystals and droplet evaporation.

The Department of Mathematics & Statistics also demonstrates expertise in population modelling & epidemiology, stochastic analysis, applied analysis and scientific computing. Access world leading mathematical and statistical Open Access research!

Explore all Strathclyde Open Access research...

Guaranteed computable bounds on quantities of interest in finite element computations

Ainsworth, M. and Rankin, R. (2012) Guaranteed computable bounds on quantities of interest in finite element computations. International Journal for Numerical Methods in Engineering, 89 (13). pp. 1605-1634. ISSN 0029-5981

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

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.