Finite Element, Discontinuous Galerkin, and Finite Difference Evolution Schemes in Spacetime

Details Finite Element, Discontinuous Galerkin, and Finite Difference Evolution Schemes in Spacetime Finite Element, Discontinuous Galerkin, and Finite Difference Evolution Schemes in Spacetime

2009-01-07

arxiv.org/abs/0901.0851v2

Class.Quant.Grav.26:175011,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

final version

Scientific paper

10.1088/0264-9381/26/17/175011

Numerical schemes for Einstein's vacuum equation are developed. Einstein's equation in harmonic gauge is second order symmetric hyperbolic. It is discretized in four-dimensional spacetime by Finite Differences, Finite Elements, and Interior Penalty Discontinuous Galerkin methods, the latter related to Regge calculus. The schemes are split into space and time and new time-stepping schemes for wave equations are derived. The methods are evaluated for linear and non-linear test problems of the Apples-with-Apples collection.

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