Title: On Triangle Inequality Based Approximation Error Estimation,
Abstract: The distance between the true and numerical solutions in some metric is
considered as the discretization error magnitude. If error magnitude ranging is
known, the triangle inequality enables the estimation of the vicinity of the
approximate solution that contains the exact one (exact solution enclosure).
The analysis of distances between the numerical solutions enables
discretization error ranging, if solutions errors are significantly different.
Numerical tests conducted using the steady supersonic flows, governed by the
two dimensional Euler equations, demonstrate the properties of the exact
solution enclosure. The set of solutions generated by solvers of different
orders of approximation is used. The success of this approach depends on the
choice of metric.