  The goal of the present paper is to prove that if a weak limit of a
consistent approximation scheme of compressible complete Euler system in the
full space $ \mathbb{R}^d,\; d=2,3 $ is a weak solution of the system then
eventually the approximate solutions converge strongly in suitable norms
locally under a minimal assumption on the initial data of the approximate
solutions. The class of consistent approximate solutions is quite general
including the vanishing viscosity and heat conductivity limit. In particular,
they may not satisfy the minimal principle for entropy.
