Multiscale and residual-free bubble functions for reaction-advection-diffusion problems

We propose a finite element method based on enriching the Galerkin approximation spaces with a combination of multiscale functions and residual-free bubbles (RFB). This approach is presented as a Petrov-Galerkin method and applied to the singularly perturbed reaction-advection-diffusion model. Numerical tests confirm that switching RFB by suitable multiscale functions in the elements connected to the outflow boundaries of the domain improves the accuracy of the solution in this region.