Finite Elements III

Part I: Fundamentals, mathematical background and problem statements 1. Prototypical fluid mechanics equations: the advection(-diffusion), Burgers, Stokes and Navier-Stokes equations 2. Relevant components of functional analysis theory 3. Analysis of the model equations with emphasis on the challenges of finite element formulations Part II: Solution strategies 1. Stabilized methods; Galerkin least-squares (GLS), artificial diffusion, streamline-upwind Petrov-Galerkin (SUPG) 2. Suitable interpolation pairs in mixed methods (e.g. Taylor-Hood) 3. Discontinuous Galerkin methods Part III: Multiscale modeling 1. A short introduction to the physics of turbulence 2. Classical turbulence models: Reynolds-averaged Navier-Stokes (RANS) and large eddy simulation (LES) 3. The variational multiscale method