Large time step asymptotic preserving evolution Galerkin methods for multidimensional system of hyperbolic balance laws.

• Applicants: Professorin Dr. Maria Lukacova; Professor Dr. Sebastian Noelle
• Subject Area: Mathematics
• Term: from 2008 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 70878602

The aim of the proposed project is the development of new adaptive semi-implicit finite volume evolution Galerkin (FVEG) methods for two- and three-dimensional systems of hyperbolic balance laws. These schemes are based on exact and approximate evolution operators, derived from bicharacteristic theory of hyperbolic conservation laws. For a number of test problems conducted over several years, these schemes have proven to be particularly accurate and efficient. The proposal intends to develop the schemes further to make them suitable for a range of hydraulic, geophysical and meteorological applications in two and three space dimensions. Key techniques to be developed are semi-implicit time approximation, adaptivity and error control, as well as multidimensional open boundary conditions. To assure that the derived schemes are robust and reliable for such complex models, an in-depth numerical analysis including stability, convergence and error control is necessary.

• DFG Programme: Research Grants