On A Posteriori Estimation of the Approximation ErrorNorm for an Ensemble of Independent Solutions

An ensemble of independent numerical solutions makes it possible to construct a hypersphere around an approximate solution that contains the true solution. The analysis is based on some geometry considerations, such as the triangle inequality and the measure concentration in spaces of large dimensions. As a result, a nonintrusive postprocessor providing error estimation on an ensemble of solutions can be constructed. Some numerical tests for the two-dimensional compressible Euler equations are given to demonstrate the properties of such postprocessing.