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Andrea Cangiani, Endre Süli:

A-posteriori error estimators and RFB

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 implemention 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.