English

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}
}

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final version

R2 v1 2026-06-21T11:58:20.171Z