A multiscale finite element space–time discretization method for transient transport phenomena using bubble functions

A space–time finite element discretization method for unsteady transport phenomena is formulated using a variational multiscale finite element scheme. The described discretization is based on the utilization of bubble function enriched finite elements. The scheme is applied to model unsteady diffusion and convection–diffusion equations. It is shown that any temporal and spatial instabilities can be removed by appropriate enrichment of linear Lagrangian finite element approximations in the context of the standard Galerkin method. The proposed scheme is compared with widely used θ time stepping method. Numerical results generated by the proposed scheme are validated via their comparison with the analytical solution of a bench mark problem.