The estimation of approximation error using inverse problem and a set of numerical solutions

Abstract

In this paper, we consider the inverse problem for the estimation of a point-wise approximation error occurring at the discretization of the system of partial differential equations. We analyse the set of the solutions, obtained by the numerical algorithms of the dissimilar structures on the same grid. The differences between the numerical solutions are used as the input data for 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 comparison of the estimated error and the exact error, obtained by subtraction of numerical and analytic solutions, is presented.