Multi-scale finite element modelling using bubble function method for a convection–diffusion problem

Due to the multi-scale nature of the convection–diffusion equation the standard Galerkin method fails to predict accurate and stable results. A multi-scale finite element method based on the bubble function approach has been developed and applied to this problem. Finite element formulations based on the discontinuous weighting functions including the streamline upwind Petrov–Galerkin (SUPG) method are also evaluated. The results show that the multi-scale method provides stable and accurate results and matches very well the analytical solution.