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The Inverse Problem for the estimation of a point-wise approximation erroroccurring at the discretization and solving of the system of partialdifferential equations is addressed. The set of the differences between thenumerical solutions is used as the input data. The analyzed solutions areobtained by the numerical algorithms of the distinct inner structure on thesame grid. The approximation error is estimated by the Inverse Problem, whichis posed in the variational statement with the zero order Tikhonovregularization. The numerical tests, performed for the two dimensional inviscidcompressible flows corresponding to Edney-I and Edney-VI shock waveinterference modes, are provided. The analyzed flowfields are computed usingten different numerical algorithms. The comparison of the estimatedapproximation error and the true error, obtained by subtraction of numericaland analytic solutions, is presented.

The Estimation of Approximation Error using the Inverse Problem and the Set of Numerical Solutions