A-posteriori error estimators and RFB - Cangiani, A; Suli, E (Unspecified, 2004)
We derive a posteriori bounds for the residual-free bubble (RFB) method for the solution of convection-dominated diffusion equations. Both linear functional error control and energy norm error control are considered. The implementation of a reliable and efficient $h$ adaptive algorithm is discussed. Finally, we proposed an $hb$ adaptive algorithm in which the local bubble stabilisation is automatically turned off ($b$ derefinement) in large parts of the computational domain during the $h$ refinement process, without compromising the accuracy of the method. The first author acknowledges the financial support of INdAM and EPSRC.