A Posteriori Error Estimation via Differences of Numerical Solutions

Alekseev, Aleksey K.; Bondarev, Alexander E.; Kuvshinnikov, Artem E.

In this work we address the problem of the estimation of the approximation error that arise at a discretization of the partial differential equations. For this we take advantage of the ensemble of numerical solutions obtained by independent numerical algorithms. To obtain the approximation error, the differences between numerical solutions are treated in the frame of the Inverse Problem that is posed in the variational statement with the zero order regularization. In this work we analyse the ensemble of numerical results that is obtained by five OpenFOAM solvers for the inviscid compressible flow around a cone at zero angle of attack. We present the comparison of approximation errors that are obtained by the Inverse Problem, and the exact error that is computed as the difference of numerical solutions and a high precision solution.