Estimation of the Distance between True and Numerical Solutions


Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

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.

About the authors

A. K. Alekseev

Moscow Institute of Physics and Technology

Author for correspondence.
Email: alekseev.ak@phystech.edu
Russian Federation, Dolgoprudnyi, Moscow oblast, 141700

A. E. Bondarev

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Author for correspondence.
Email: bond@keldysh.ru
Russian Federation, Moscow, 125047

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2019 Pleiades Publishing, Ltd.