25th Annual GAMM-Seminar Leipzig on

FEM and BEM for time-dependent wave problems

Numerical Schemes in Space-Time for the Einstein equations

Gerhard Zumbusch (Friedrich-Schiller-Universität Jena)

The Einstein equations describe the metric of curved space-time in general relativity. They are second order quasi-linear wave equations. In harmonic gauge, they are symmetric hyperbolic. Together with smooth initial data this leads to a well-posed Cauchy problem. Linearized around flat space Minkowski metric, the Einstein equations can be reduced to a D'Alembert equation for a divergence free tensor field, which can be considered as a generalization of the Maxwell equation. We derive a variational formulation of the Einstein equation second order in space and time, discretize in space-time with finite differences, finite elements, or discontinuous Galerkin schemes, split space and time and finally derive several time-stepping schemes. The methods are evaluated for linear and non-linear test problems.

Impressum Valid HTML 4.0 Transitional