1 Computational Fluid Dynamics Reading Group : Finite Element Methods for Stokes & The Inf

Last week we studied the key concepts of Finite Element Methods, in the context of solving the Laplace equation. We saw the …nite element method arise naturally as an instance of the Galerkin method, a discretization procedure for the corresponding weak formulation. Finally, we learned about error estimates, examples of elements and implementation practices. This week, our main objective is to do the same in the context of solving the Stokes equation, which as we know is the low Reynolds number limit of the Navier Stokes equation. The theory and implementation behind the Finite Element Methods used to solve this equation (which are referred to in the literature asMixed Methods) are much more simpler than their counterparts for Navier Stokes (since one has to deal with the nonlinearity and the time dependance, amongst other numerical issues) and yet capture their essential components.