2017/08/15 by A. K. Alekseev, Alekseev, A. K., А. Е. Бондарев +3
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.1708.04604
openalex publication_date 2017/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The distance between the true and numerical solutions in some metric is considered as the discretization error magnitude. If error magnitude ranging is known, the triangle inequality enables the estimation of the vicinity of the approximate solution that contains the exact one (exact solution enclosure). The analysis of distances between the numerical solutions enables discretization error ranging, if solutions errors are significantly different. Numerical tests conducted using the steady supersonic flows, governed by the two dimensional Euler equations, demonstrate the properties of the exact solution enclosure. The set of solutions generated by solvers of different orders of approximation is used. The success of this approach depends on the choice of metric.