Pacific Northwest Numerical Analysis Seminar
October 13, 2007


Exactly divergence-free discontinuous Galerkin methods for incompressible fluid flow problems

Dominik Schoetzau
Department of Mathematics
University of British Columbia

We present and analyze exactly divergence-free discontinuous Galerkin finite element methods for the discretization of linear convection-diffusion problems. The main advantages of these methods in comparison with standard conforming finite element approaches lie in their robustness in transport-dominated regimes, their local conservation properties, their flexibility in the mesh-design, and their exact satisfaction of the incompressibility constraint. We derive the methods for the incompressible Navier-Stokes equations, discuss their stability properties and carry out their numerical analysis. We also present numerical results that confirm the theoretical results and highlight the advantages of these methods.


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