Fully computable a posteriori error bounds for stabilised FEM approximations of convection–reaction–diffusion problems in three dimensions
Article first published online: 24 JUL 2013
Copyright © 2013 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids
Volume 73, Issue 9, pages 765–790, 30 November 2013
How to Cite
Ainsworth, M., Allendes, A., Barrenechea, G. R. and Rankin, R. (2013), Fully computable a posteriori error bounds for stabilised FEM approximations of convection–reaction–diffusion problems in three dimensions. Int. J. Numer. Meth. Fluids, 73: 765–790. doi: 10.1002/fld.3822
- Issue published online: 9 OCT 2013
- Article first published online: 24 JUL 2013
- Manuscript Accepted: 21 MAY 2013
- Manuscript Revised: 8 MAY 2013
- Manuscript Received: 19 JUN 2012
- 3D convection–reaction–diffusion;
- SUPG stabilised method;
- fully computable a posteriori error estimator
Fully computable upper bounds are developed for the discretisation error measured in the natural (energy) norm for convection–reaction–diffusion problems in three dimensions. The upper bounds are genuine upper bounds in the sense that the numerical value of the estimated error exceeds the actual numerical value of the true error regardless of the coarseness of the mesh or the nature of the data for the problem. All constants appearing in the bounds are fully specified. Examples show the estimator to be reliable and accurate even in the case of complicated three-dimensional problems. Copyright © 2013 John Wiley & Sons, Ltd.