Asymptotic errors in the superconvergence of discontinuous Galerkin methods based on upwind-biased fluxes for 1D linear hyperbolic equations

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Authors
Lu, Tianshi
Rahmati, Sirvan
Advisors
Issue Date
2024
Type
Article
Keywords
Asymptotic error , Discontinuous Galerkin , Postprocessing , Superconvergence , Upwind-biased flux
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Lu, T., Rahmati, S. Asymptotic errors in the superconvergence of discontinuous Galerkin methods based on upwind-biased fluxes for 1D linear hyperbolic equations. (2024). Matematica. DOI: 10.1007/s44007-024-00093-2
Abstract

In this paper, we study the superconvergence of the semi-discrete discontinuous Galerkin (DG) method for linear hyperbolic equations in one spatial dimension. The asymptotic errors in cell averages, downwind point values, and the postprocessed solution are derived for the initial discretization by Gaussian projection (for periodic boundary condition) or Cao projection Cao et al. (SIAM J. Numer. Anal. 5, 2555-2573 (2014)) (for Dirichlet boundary condition). We proved that the error constant in the superconvergence of order 2k+1 for DG methods based on upwind-biased fluxes depends on the parity of the order k. The asymptotic errors are demonstrated by various numerical experiments for scalar and vector hyperbolic equations. © The Author(s) 2024.

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Publisher
Springer
Journal
Matematica
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https://hdl.handle.net/10057/27891
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DOI
10.1007/s44007-024-00093-2
ISSN
2730-9657
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MATH Research Publications