Predictor-Multicorrector Scheme for the Dynamic Diffusion Method

In this work we evaluate a predictor-multicorrector integration scheme for transient advection-diffusion-reaction problems using the Dynamic Diffusion method (DD). This multiscale finite element formulation results in a free parameter method in which the subgrid scale space is defined using bubble functions whose degrees of freedom are locally eliminated in favor of the degrees of freedom that live on the resolved scales. The time advancing scheme assumes that the subscales change in time. The formulation is compared with the Consistent Upwind Petrov-Galerkin (CAU) method using the same predictor-multicorrector scheme. Numerical experiments based on benchmark 2D problems were conducted to illustrate the behavior of this new algorithm applied to advection-diffusion-reaction equations.