68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section {04 in that areag 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

In the following an introduction to the level set method will be givenso that one becomes aware of the arising problems, which lead to the needof reinitialization. The problems concerning reinitialization itself will be analysed more detailed and a solution for area loss will be proposed. This solution consists in a combination of the commonly used PDE for reinitialization and extrapolation around the zero level set. Numericalexperiments show rather satisfactory results as far as area loss and computation of curvature are concerned.

In this article we present a method to extend high order finite volume schemes
to networks of hyperbolic conservation laws with algebraic coupling conditions. This method is based on an ADER approach in time to solve the
generalized Riemann problem at the junction. Additionally to the high order accuracy, this approach maintains an exact conservation of quantities if
stated by the coupling conditions. Several numerical examples confirm the
benefits of a high order coupling procedure for high order accuracy and stable
shock capturing.