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arXiv · 0901.0851

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

Gerhard Zumbusch
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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.

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Gerhard Zumbusch. 2009-07-20. Finite Element, Discontinuous Galerkin, and Finite Difference Evolution Schemes in Spacetime. https://doi.org/10.1088/0264-9381%2F26%2F17%2F175011

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