Linear schemes with several degrees of freedom for the 1D transport equation

Abstract:

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 (L_{2}-projection for example) by O(h^{p}). This fact leads to an algorithm establishing the optimal values p and q for a given scheme.

Keywords:

consistency and accuracy, superconvergence

Publication language:russian, страниц:40

Research direction:

Mathematical problems and theory of numerical methods