A-posteriori error estimators and RFB

Abstract

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 adaptive algorithm is discussed. Finally, we proposed an adaptive algorithm in which the local bubble stabilisation is automatically turned off ( derefinement) in large parts of the computational domain during the refinement process, without compromising the accuracy of the method.

The first author acknowledges the financial support of INdAM and EPSRC.