UBC Theses and Dissertations
An exactly divergence-free finite element method for non-isothermal flow problems Qin, Tong
In this thesis the exactly divergence-free finite element method developed by Cockburn, Scheotzau and Kanschat in  and  is studied. This method is first reviewed in the context of Stokes problem. An interior penalty discontinuous Galerkin approach is formulated and analysed in the unified framework established in ,  and . Then we extend the method to non-isothermal flow problems, in particular, to a generalised Boussinesq equation. Following the work by Ricardo, Scheotzau and Qin in , the method is formulated and the numerical analysis is reviewed. Numerical examples are implemented and presented, which verify the theoretical error estimates and the exactly divergence-free property.
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