时空中的有限元、间断Galerkin和有限差分演化格式
Finite Element, Discontinuous Galerkin, and Finite Difference Evolution Schemes in Spacetime
摘要：
发展了爱因斯坦真空方程的数值格式。简谐规范中的爱因斯坦方程是二阶对称双曲方程。它在四维时空中通过有限差分、有限元和内部罚间断伽辽金方法离散化，后者与Regge演算有关。该计划被分裂成空间和时间和新的时间推进格式的波动方程。的方法进行评估的线性和非线性测试问题的苹果与苹果收集。
英文摘要：
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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