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KIAM Preprint № 73, Moscow, 2019
Authors: Bakhvalov P.A., Surnachev M.D.
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(hp + thq) 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(hp). 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
Russian source text:
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