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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Discontinuous Galerkin error estimation for linear symmetrizable hyperbolic systems
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by Slimane Adjerid and Thomas Weinhart PDF
Math. Comp. 80 (2011), 1335-1367 Request permission

Abstract:

We present an a posteriori error analysis for the discontinuous Galerkin discretization error of first-order linear symmetrizable hyperbolic systems of partial differential equations with smooth solutions. We perform a local error analysis by writing the local error as a series and showing that its leading term can be expressed as a linear combination of Legendre polynomials of degree $p$ and $p+1$. We apply these asymptotic results to show that projections of the error are pointwise $\mathcal {O}(h^{p+2})$-superconvergent. We solve relatively small local problems to compute efficient and asymptotically exact estimates of the finite element error. We present computational results for several linear hyperbolic systems in acoustics and electromagnetism.
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Additional Information
  • Slimane Adjerid
  • Affiliation: Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
  • Thomas Weinhart
  • Affiliation: Department of Applied Mathematics, University of Twente, 7500 AE Enschede, The Netherlands
  • Received by editor(s): September 10, 2009
  • Received by editor(s) in revised form: June 17, 2010
  • Published electronically: January 25, 2011
  • Additional Notes: This research was partially supported by the National Science Foundation (Grant Numbers DMS 0511806, DMS 0809262).
  • © Copyright 2011 American Mathematical Society
  • Journal: Math. Comp. 80 (2011), 1335-1367
  • MSC (2010): Primary 65M60, 65N35; Secondary 35L50
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02460-9
  • MathSciNet review: 2785461