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


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Volker J., KAYA MERDAN S. , Layton W.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, cilt.195, ss.4594-4603, 2006 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 195
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.cma.2005.10.006
  • Dergi Adı: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
  • Sayfa Sayıları: ss.4594-4603

Özet

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. (c) 2005 Elsevier B.V. All rights reserved.