General relativity, partial differential equations, numerical methods.
KEY RATIO
3+1 decomposition
ADM divides geometry into spatial metrics, extrinsic curvature, lapse and shift. Hamiltonian and impulse constraints must be satisfied along with the evolution.
Formulation and calibration
BSSN and generalized harmonic use different variables and constraint management mechanisms. The choice of coordinates affects the stability and interpretation of the grid, but should not change the physical observables in the convergent solution.
Convergence
Compare multiple resolutions with the same physical parameters. The given estimate of p is applicable in the asymptotic mode for a geometrically decreasing step with the ratio q>1; Differences close to zero require caution.
Verification
Check constraint norms, boundary conditions, conservation, and known exact solutions. A bright mesh animation without these checks is not verified numerical relativity.
Test yourself
Check-ins are only saved in your browser. They do not replace a teacher's review of a solution.
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This is an introductory route and is not a replacement for a full university course. Always check the conventions, premises and scope of the formula you are using.