Zurück zu den Preprints des Jahres 2005


A Two-Level Variational Multiscale Method for Convection-Diffusion Equations

by John, Volker, Kaya, Songul, Layton, William.

Series: 2005-04, Preprints

65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

This paper studies the error in, the efficient implementation
of and time stepping methods for a variational multiscale method (VMS) for solving
convection-dominated problems. The VMS studied uses a fine mesh $C^0$ finite
element space $X^h$ to approximate the concentration and a coarse mesh discontinuous
vector finite element space $L^H$ for the large scales of the flux in the two scale
discretization. Our tests show that these choices lead to an efficient 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 effects across
scales are tested and compared. The semi-implicit VMS was much more efficient. The
observed global accuracy of the most straightforward VMS implementation was much
better than the artificial diffusion stabilization and comparable to a
streamline-diffusion finite element method in our tests.

convection-dominated convection-diffusion equation, variational multiscale method, two-level method, efficient implementation