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. Bubble functions are added to the ordinary Lagrange shape functions using either residual free bubble (RFB) functions or other simpler bubble functions in conjunction with the static condensation (STC) methods. To validate the approach, the numerical results obtained for a benchmark problem are compared with their corresponding analytical solution. Further numerical experiments are carried out to investigate the performance of the developed scheme over a range of Peclet and Damkohler numbers for productive and dissipative reaction cases.