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A Simple Explanation of Superconvergence for Discontinuous Galerkin Solutions to ut+ux=0

Part of: Hyperbolic equations and systems Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  08 March 2017

Philip Roe
Philip Roe*
Affiliation:
Department of Aerospace Engineering, University of Michigan, Ann Arbor 48109, USA
*
*Corresponding author. Email address:philroe@umich.edu (P. L. Roe)
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Abstract

The superconvergent property of the Discontinuous Galerkin (DG) method for linear hyperbolic systems of partial differential equations in one dimension is explained by relating the DG method to a particular continuous method, whose accuracy depends in part on a local analysis, and in part on information transferred from upwind elements.

Keywords

Linear advectiondiscontinuous Galerkinsuperconvergence

MSC classification

Secondary: 35L03: Initial value problems for first-order hyperbolic equations 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 4 , April 2017 , pp. 905 - 912
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Chi-Wang Shu

References

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