A Comparison of the Richardson Extrapolation and the Approximation Error Estimation on the Ensemble of Numerical Solutions

The epistemic uncertainty quantification concerning the estimation of the approximation error using the differences between numerical solutions treated in the Inverse Problem statement is addressed and compared with the Richardson extrapolation. The Inverse Problem is posed in the variational statement with the zero order Tikhonov regularization. The ensemble of numerical results, obtained by the OpenFOAM solvers for the inviscid compressible flow with a shock wave is analyzed. The approximation errors, obtained by the Richardson extrapolation and the Inverse Problem are compared with the exact error, computed as the difference of numerical solutions and the analytical solution. The Inverse problem based approach is demonstrated to be an inexpensive alternative to the Richardson extrapolation.