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• W2523009454 abstract "In this paper, an analysis of the accuracy-enhancement for the discontinuous Galerkin (DG) method applied to one-dimensional scalar nonlinear hyperbolic conservation laws is carried out. This requires analyzing the divided difference of the errors for the DG solution. We therefore first prove that the $$alpha $$ -th order $$(1 le alpha le {k+1})$$ divided difference of the DG error in the $$L^2$$ norm is of order $${k + frac{3}{2} - frac{alpha }{2}}$$ when upwind fluxes are used, under the condition that $$|f'(u)|$$ possesses a uniform positive lower bound. By the duality argument, we then derive superconvergence results of order $${2k + frac{3}{2} - frac{alpha }{2}}$$ in the negative-order norm, demonstrating that it is possible to extend the Smoothness-Increasing Accuracy-Conserving filter to nonlinear conservation laws to obtain at least $$({frac{3}{2}k+1})$$ th order superconvergence for post-processed solutions. As a by-product, for variable coefficient hyperbolic equations, we provide an explicit proof for optimal convergence results of order $${k+1}$$ in the $$L^2$$ norm for the divided differences of DG errors and thus $$({2k+1})$$ th order superconvergence in negative-order norm holds. Numerical experiments are given that confirm the theoretical results." @default.
• W2523009454 created "2016-09-30" @default.
• W2523009454 creator A5004641328 @default.
• W2523009454 creator A5088340901 @default.
• W2523009454 date "2016-08-08" @default.
• W2523009454 modified "2023-10-14" @default.
• W2523009454 title "Discontinuous Galerkin methods for nonlinear scalar hyperbolic conservation laws: divided difference estimates and accuracy enhancement" @default.
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• W2523009454 doi "https://doi.org/10.1007/s00211-016-0833-y" @default.
• W2523009454 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/5445630" @default.
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