Enhanced RFB method

Abstract

The residual-free bubble method (RFB) is a parameter-free stable finite element method that has been applied successfully to solve a wide range of boundary-value problems presenting multiple-scale behavior. If some local features of the solution are known a-priori, the RFB finite element space approximation properties can be increased by enriching it on some specific edges of the partition (see[7]). Based on such idea, we define and analyse the enhanced residual-free bubbles method for the solution of convection-dominated convection-diffusion problems in 2-D. Our a-priori analysis enlightens the limitations of the RFB method and the superior global convergence properties of the new method. The theoretical results are supported by extensive numerical experimentation.\ud \ud The first author acknowledges the financial support of INdAM and EPSR