2003/04/17 by Manuel Tiglio, Tiglio, Manuel
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Dynamics and Fractals #Stability and Controllability of Differential Equations #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0304062
arxiv created 2003/04/17 · openalex publication_date 2003/04/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I present a new, simple method to dynamically control the growth of the discretized constraints during a free evolution of Einstein's equations. During an evolution, any given family of formulations is adjusted off the constraints surface in a way such that, for any chosen numerical method and arbitrary but fixed resolution, the constraints growth can be minimized with respect to the freedom allowed by the formulation. In particular, provided there is enough freedom, the discretized constraints can be maintained close to its initial truncation value for all times, or decay from it. No a priori knowledge of the solution is needed, and the method can be applied to any formulation of Einstein's equations without affecting hyperbolicity. This method is independent of the numerical algorithm and accounts for constraint violating modes introduced both by continuum instabilities of the formulation and by the numerical method.