A Two-Level Variational Multiscale Method for Convection-Diusion Equations
Volker John, Songül Kaya, William Layton · 2005
This paper studies the error in, the ecien t implementation of and time stepping methods for a variational multiscale method (VMS) for solving convectiondominated problems. The VMS studied uses a ne mesh C 0 nite element space X h to approximate the concentration and a coarse mesh discontinuous vector nite element space L H for the large scales of the ux in the two scale discretization. Our tests show that these choices lead to an ecien t VMS whose complexity is further reduced if a (locally) L 2 -orthogonal basis for L H is used. A fully implicit and a semi-implicit treatment of the terms which link eects across scales are tested and compared. The semi-implicit VMS was much more ecien t. The observed global accuracy of the most straightforward VMS implementation was much better than the articial diusion stabilization and comparable to a streamline-diusi on nite element method in our tests.