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The dynamics of gravitational waves is investigated in full 3+1 dimensionalnumerical relativity, emphasizing the difficulties that one might encounter innumerical evolutions, particularly those arising from non-linearities and gaugedegrees of freedom. Using gravitational waves with amplitudes low enough thatone has a good understanding of the physics involved, but large enough toenable non-linear effects to emerge, we study the coupling between numericalerrors, coordinate effects, and the nonlinearities of the theory. We discussthe various strategies used in identifying specific features of the evolution.We show the importance of the flexibility of being able to use differentnumerical schemes, different slicing conditions, different formulations of theEinstein equations (standard ADM vs. first order hyperbolic), and differentsets of equations (linearized vs. full Einstein equations). A non-linear scalarfield equation is presented which captures some properties of the full Einsteinequations, and has been useful in our understanding of the coupling betweenfinite differencing errors and non-linearites. We present a set of monitoringdevices which have been crucial in our studying of the waves, including Riemanninvariants, pseudo-energy momentum tensor, hamiltonian constraint violation,and fourier spectrum analysis.Comment: 34 pages, 14 figure

Dynamics of gravitational waves in 3D: Formulations, methods, and tests