Finite Element, Discontinuous Galerkin, and Finite Difference Evolution Schemes in Spacetime
General Relativity and Quantum Cosmology
2009-08-17 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0901.0851,
title = {Finite Element, Discontinuous Galerkin, and Finite Difference Evolution Schemes in Spacetime},
author = {Gerhard Zumbusch},
journal= {arXiv preprint arXiv:0901.0851},
year = {2009}
}
Comments
final version