Finite Volume methods are the standard numerical methods for the solution of conservation laws, which represent fundamental laws of physics. Of particular importance is their use to model fluid flows in the form of parabolic and hyperbolic partial differential equations.

The course explains basic pitfalls of numerical methods for these equations and how to arrive at stable and convergent finite volume methods of first order. This is then extended to multiple dimensions and higher order methods in the form of Discontinuous Galerkin methods, which are currently a hot research topic.