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.
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FUNDING
This work was supported by the Russian Foundation for Basic Research, projects no. 17-01-444A.
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Translated by I. Ruzanova
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Alekseev, A.K., Bondarev, A.E. Estimation of the Distance between True and Numerical Solutions. Comput. Math. and Math. Phys. 59, 857–863 (2019). https://doi.org/10.1134/S0965542519060034
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DOI: https://doi.org/10.1134/S0965542519060034