Abstract
The residual-free bubble method (RFB) is a parameter-free stable finite element method that has been successfully applied to a wide range of boundary-value problems exhibiting multiple-scale behaviour. If some local features of the solution are known a priori, the approximation properties of the RFB finite element space can be improved by enriching it on selected edges of the partition by edge-bubbles that are supported on pairs of neighbouring elements. Motivated by this idea, we define and analyse an enhanced residual-free bubble method for the solution of convection-dominated convection-diffusion problems in 2-D. Our a priori analysis highlights the limitations of the RFB method and the improved global approximation properties of the new method. The theoretical results are supported by detailed numerical experiments.
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