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This article is cited in 5 scientific papers (total in 5 papers)
On a posteriori estimation of the approximation error norm for an ensemble of independent solutions
A. K. Alekseev, A. E. Bondarev Keldysh Institute of Applied Mathematics, Russian Academy of Sciences,
Miusskaya pl. 4, Moscow, 125047 Russia
Abstract:
An ensemble of independent numerical solutions enables one to construct a hypersphere around the approximate solution that contains the true solution. The analysis is based on some geometry considerations,
such as the triangle inequality and the measure concentration in the spaces of large dimensions. As a result,
there appears the feasibility for non-intrusive postprocessing that provides the error estimation on the ensemble of solutions. The numerical tests for two-dimensional compressible Euler equations are provided that
demonstrates properties of such postprocessing.
Key words:
discretization error, ensemble of numerical solutions, measure concentration, Euler equations.
Received: 06.09.2018 Revised: 07.05.2019 Accepted: 16.04.2020
Citation:
A. K. Alekseev, A. E. Bondarev, “On a posteriori estimation of the approximation error norm for an ensemble of independent solutions”, Sib. Zh. Vychisl. Mat., 23:3 (2020), 233–248; Num. Anal. Appl., 13:3 (2020), 195–206
Linking options:
https://www.mathnet.ru/eng/sjvm745 https://www.mathnet.ru/eng/sjvm/v23/i3/p233
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Abstract page: | 144 | Full-text PDF : | 45 | References: | 24 | First page: | 8 |
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