  The Inverse Problem for the estimation of a point-wise approximation error
occurring at the discretization and solving of the system of partial
differential equations is addressed. The set of the differences between the
numerical solutions is used as the input data. The analyzed solutions are
obtained by the numerical algorithms of the distinct inner structure on the
same grid. The approximation error is estimated by the Inverse Problem, which
is posed in the variational statement with the zero order Tikhonov
regularization. The numerical tests, performed for the two dimensional inviscid
compressible flows corresponding to Edney-I and Edney-VI shock wave
interference modes, are provided. The analyzed flowfields are computed using
ten different numerical algorithms. The comparison of the estimated
approximation error and the true error, obtained by subtraction of numerical
and analytic solutions, is presented.
