New mathematical models and numerical algorithms for Newtonian and general relativistic continuum physics, Michael Dumbser, Università di Trento

In the first part of the talk we present high order arbitrary high order accurate (ADER) finite volume and discontinuous Galerkin finite element schemes for the numerical solution of a new unified first order symmetric hyperbolic and thermodynamically compatible (SHTC) formulation of Newtonian continuum physics.

In the second part of the talk, we show a successful extension of the GPR model to general relativity, leading to a novel and unified first order hyperbolic formulation of general relativistic continuum mechanics. In the last part of the talk we introduce a new, provably strongly hyperbolic first order reduction of the CCZ4 formalism of the Einstein field equations of general relativity and its solution with high order ADER discontinuous Galerkin finite element schemes.