An estimation of point-wise approximation error using the set of numerical solutions

The present paper is addressed to the estimation of the local (point-wise) approximation error on the ensemble of the numerical solutions obtained using independent algorithms. The variational inverse problem is posed for the approximation error estimation. The considered problem is ill-posed due to invariance of the governing equations to the shift transformations. By this reason, the zero order Tikhonov regularization is applied. The numerical tests for the two-dimensional equations describing the inviscid compressible flow are performed in order to verify the efficiency of considered algorithm. The estimates of approximation errors, obtained by the considered inverse problem, demonstrate the satisfactory accordance with the Richardson extrapolation results at significantly less computational costs.