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Register a new userSuperconvergence of local discontinuous Galerkin methods with generalized alternating fluxes for 1D linear convection-diffusion equations
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Xiong Meng
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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This paper investigates superconvergence properties of the local discontinuous Galerkin methods with generalized alternating fluxes for one-dimensional linear convection-diffusion equations. By the technique of constructing some special correction functions, we prove the $(2k+1)$th order superconvergence for the cell averages, and the numerical traces in the discrete $L^2$ norm. In addition, superconvergence of order $k+2$ and $k+1$ are obtained for the error and its derivative at generalized Radau points. All theoretical findings are confirmed by numerical experiments.
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