Using bubble functions in the multi-scale finite element modeling of the convection–diffusion–reaction equation

The Convection–diffusion–reaction (CDR) equation shows multi-scale behaviour in cases where it represents convection or reaction dominated transport processes. Bubble function enriched finite elements are used to generate stable and accurate solutions for this equation. To validate the approach, the numerical results obtained for a benchmark problem are compared with their corresponding analytical solution for both exponential and propagation regimes.