Estimation of the Distance between True and Numerical Solutions


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Resumo

Given an ensemble of numerical solutions generated by different algorithms that are guaranteed to have different errors, the triangle inequality is used to find a neighborhood of a numerical solution that contains the true one. By analyzing the distances between the numerical solutions, the latter can be ranged according to their error magnitudes. Numerical tests for the two-dimensional compressible Euler equations demonstrate the possibility of comparing the errors of different methods and determining a domain containing the true solution.

Sobre autores

A. Alekseev

Moscow Institute of Physics and Technology

Autor responsável pela correspondência
Email: alekseev.ak@phystech.edu
Rússia, Dolgoprudnyi, Moscow oblast, 141700

A. Bondarev

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Autor responsável pela correspondência
Email: bond@keldysh.ru
Rússia, Moscow, 125047

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