Estimation of the Distance between True and Numerical Solutions
- Authors: Alekseev A.K.1, Bondarev A.E.2
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Affiliations:
- Moscow Institute of Physics and Technology
- Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
- Issue: Vol 59, No 6 (2019)
- Pages: 857-863
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/180608
- DOI: https://doi.org/10.1134/S0965542519060034
- ID: 180608
Cite item
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
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