On Estimation of Numerical Solution in Prager&Synge Sense

The numerical solution in sense of Prager&Synge is defined as a hypersphere containing a true solution of a system of partial differentiation equations (PDE). In the original variant Prager&Synge method is based on special orthogonal properties of PDE and may be applied only to several equations. Herein, the Prager&Synge solution (center and radius of the hypersphere) is estimated using the ensemble of numerical solutions obtained by independent algorithms. This approach is not problem dependent and may be applied to arbitrary system of PDE. Several options for computation of the Prager&Synge solution are considered. The first one is based on the search for the orthogonal truncation errors and their transformation. The second is based on the orthogonalization of approximation errors obtained using the defect correction method. It applies the superposition of numerical solutions. The third option uses the width of the ensemble of numerical solutions. The numerical tests for the two dimensional inviscid flows are presented that demonstrate the acceptable effectivity of the approximation error estimates based on the solution in the Prager&Synge sense.