Knowledge of standard numerical methods for the approximation of solutions of ordinary and partial differential equations (discretization methods). Finite element methods. Discontinuous Galerkin methods. Instationary PDEs.
Initial- and boundary value problems for ordinary and partial differential equations: One-step and multi-step methods, adaptivity. Introduction to numerical methods for partial differential equations of elliptic, parabolic, and hyperbolic type. Variational formulation of PDEs and function spaces. Finite element convergence theory. Discontinuous Galerkin methods for convection dominated problems. Mixed methods and applications in fluid mechanics. Nonlinear equations and applications in solid mechanics. Vectorial function spaces and applications in electromagnetics. Instationary PDEs and time-stepping methods. Analysis of iterative solvers and preconditioners. A posteriori error estimates and adaptivity. Exercises: Apply these methods to solve pde problems; exercises with NGSolve-Python; verify qualitative and quantitative properties.