Traditionally Hermite finite elements have been used to solve fourth or higher order boundary value PDE's, for in this case minimum continuity of solution derivatives must be ensured. It turns out that nothing prevents this kind of methods from being used to solve second order boundary value problems, provided solutions are sufficiently smooth. In this talk we show some advantages Hermite finite elements bring about, in the solution of fluid flow or heat transfer problems modelled by second order PDE's. More specifically, we consider applications to the convection-diffusion equations and to viscous incompressible flow.
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