The features of the of truncation and approximation errors’ geometry on the ensemble of numerical solutions
Abstract:
The truncation and approximation errors are estimated for the ensemble of numerical solutions obtained using methods based on the independent algorithms of different properties including nominal convergence orders. The angles between approximation errors of the solutions of considered ensemble are far from zero that enables a posteriori estimation of approximation error norm. Also, a posteriori error estimation may be obtained by the analysis of the distances between solutions. The methods for data treating are considered, which provide a posteriori error norm estimation with the acceptable values of the efficiency index. The results of the numerical tests for flows of inviscid compressible flow are presented. To obtain numerical results, the concept of a generalized computational experiment was used, which allows the simultaneous solution of one problem with variation of the determining parameters. Here, the choice of a solver can be considered as a determining parameter. The observed behavior of errors may be explained form the standpoint of the measure concentration phenomenon and algorithmic randomness.
