A two-level variational multiscale method for convection-dominated convection-diffusion equations

Volker, John
Kaya Merdan, Songül
Layton, William
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-O 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.


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Citation Formats
J. Volker, S. Kaya Merdan, and W. Layton, “A two-level variational multiscale method for convection-dominated convection-diffusion equations,” COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, pp. 4594–4603, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41036.