Abstract
Estimation of approximation errors on an ensemble of numerical solutions obtained by independent algorithms is addressed in the linear and nonlinear cases. In linear case the influence of the irremovable uncertainty on error estimates is considered. In nonlinear case, the nonuniform improvement of estimates’ accuracy is demonstrated that enables to overperform the quality of linear estimates. An ensemble of numerical results, obtained by four OpenFOAM solvers for the inviscid compressible flow with an oblique shock wave, is used as the input data. A comparison of approximation errors, obtained by these methods, and the exact error, computed as the difference of numerical solutions and the analytical solution, is presented. The numerical tests demonstrated feasibility to obtain the reliable error estimates (in the linear case) and to improve the accuracy of certain approximation error in the nonlinear case.
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Alekseev, A.K., Bondarev, A.E. (2023). On the Resolution of Approximation Errors on an Ensemble of Numerical Solutions. In: Mikyška, J., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2023. ICCS 2023. Lecture Notes in Computer Science, vol 14077. Springer, Cham. https://doi.org/10.1007/978-3-031-36030-5_51
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