Multiscale finite element modeling of diffusion-reaction equation using bubble functions with bilinear and triangular elements

A multiscale finite element method based on the bubble functions is used to generate stable and accurate solutions for the diffusion-reaction equation for both dissipation and production cases. This equation shows multiscale behaviour when the process becomes reaction dominated. To validate the approach, the numerical results obtained for a benchmark problem are compared with the analytical solution. Further numerical experiments are carried out to investigate the performance of the developed technique over a range Damkohler number. The numerical experiments are performed using bilinear and triangular elements.