We consider linear schemes with several degrees of freedom for the 1D transport equation. The solution error possesses the estimate O(h^p + th^q) where p is equal to or greater by one than the truncation error order and q>=p (for the discontinuous Galerkin method p = k+1 and q = 2k+1 where k is the order of polynomials). We prove that this estimate holds if and only if there exists a mappingof smooth functions on the mesh space providing the q-th order of the truncation error and deviating from the standard mapping (L₂-projection for example) by O(h^p). This fact leads to an algorithm establishing the optimal values p and q for a given scheme.

consistency and accuracy, superconvergence

Mathematical problems and theory of numerical methods

Bakhvalov Pavel Alexeevisch,  ,  orcid.org/0000-0003-3416-8277,  KIAM RAS

Surnachev Mikhail Dmitriyevich,  ,  orcid.org/0000-0003-4071-5097,  KIAM RAS