Syllabus
Rothe method for parabolic problems. Existence and regularity of solutions, discretization error of the Rothe method.
Higher order discretizations of time derivatives, discontinuous Galerkin method in time. Discretization of hyperbolic problems.
Nonstationary advection and convection problems: Gibbs phenomenon, stabilization by artificial diffusion, semi-Lagrangian methods.
Evolutionary problems on time-dependent domains: ALE method, level set methods.
Annotation
The course deals with various theoretical and practical aspects of the numerical solution of evolutionary differential equations. We proceed from purely theoretic (Rothe method) to completely practical topics (discretization of problems in time dependent domains).
The course thus represents more of an overview of various techniques connected to the numerical solution of evolutionary equations than one compact theory.