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. © 2013 John Wiley & Sons, Ltd.
|Number of pages||26|
|Journal||International Journal for Numerical Methods in Fluids|
|Publication status||Published - 30 Nov 2013|
Ainsworth, M., Allendes, A., Barrenechea, G. R., & Rankin, R. (2013). Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions. International Journal for Numerical Methods in Fluids, 765-790. https://doi.org/10.1002/fld.3822