Estimation of Pointwise Approximation Error Using a Set of Numerical Solutions

Pleiades Publishing Ltd - Tập 15 - Trang 281-292 - 2022
A. K. Alekseev1, A. E. Bondarev1
1Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

Tóm tắt

This paper deals with estimation of local (pointwise) approximation error on an ensemble of numerical solutions obtained by using independent algorithms. A variational inverse problem is posed for approximation error estimation. This problem is ill-posed due to translation-invariance of the governing equations. Zero order Tikhonov regularization is applied to obtain stable solutions. Numerical tests for two-dimensional equations describing inviscid compressible flow are performed to verify the efficiency of the algorithm. The approximation error estimates obtained by using the inverse problem are in satisfactory agreement with those obtained by Richardson extrapolation, but with significantly less computational costs.

Tài liệu tham khảo

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