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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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Convergence of discontinuous Galerkin schemes for front propagation with obstacles
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by Olivier Bokanowski, Yingda Cheng and Chi-Wang Shu PDF
Math. Comp. 85 (2016), 2131-2159 Request permission

Abstract:

We study semi-Lagrangian discontinuous Galerkin (SLDG) and Runge-Kutta discontinuous Galerkin (RKDG) schemes for some front propagation problems in the presence of an obstacle term, modeled by a nonlinear Hamilton-Jacobi equation of the form $\min (u_t + c u_x, u - g(x))=0$, in one space dimension. New convergence results and error bounds are obtained for Lipschitz regular data. These “low regularity” assumptions are the natural ones for the solutions of the studied equations. Numerical tests are given to illustrate the behavior of our schemes.
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Additional Information
  • Olivier Bokanowski
  • Affiliation: Université Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS, F-75205 Paris, France
  • MR Author ID: 605144
  • Email: boka@math.jussieu.fr
  • Yingda Cheng
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • MR Author ID: 811395
  • Email: ycheng@math.msu.edu
  • Chi-Wang Shu
  • Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
  • MR Author ID: 242268
  • Email: shu@dam.brown.edu
  • Received by editor(s): June 13, 2013
  • Received by editor(s) in revised form: July 4, 2014, and February 21, 2015
  • Published electronically: December 29, 2015
  • Additional Notes: The research of the first author was supported by the EU under the 7th Framework Programme Marie Curie Initial Training Network “FP7-PEOPLE-2010-ITN”, SADCO project, GA number 264735-SADCO.
    The research of the second author was supported by NSF grant DMS-1217563 and the start-up grant from Michigan State University.
    The research of the third author was supported by ARO grant W911NF-11-1-0091 and NSF grants DMS-1112700 and DMS-1418750.
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 2131-2159
  • MSC (2010): Primary 65-XX; Secondary 65M60, 65M12
  • DOI: https://doi.org/10.1090/mcom/3072
  • MathSciNet review: 3511277