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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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Application of generalized Gauss–Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations
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by Yao Cheng, Xiong Meng and Qiang Zhang PDF
Math. Comp. 86 (2017), 1233-1267 Request permission

Abstract:

In this paper we consider the local discontinuous Galerkin method based on the generalized alternating numerical fluxes for solving the linear convection-diffusion equations in one dimension and two dimensions. As an application of generalized Gauss–Radau projections, we get rid of the dual argument and obtain directly the optimal $L^2$-norm error estimate in a uniform framework. The sharpness of the theoretical results is demonstrated by numerical experiments.
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Additional Information
  • Yao Cheng
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, Jiangsu Province, People’s Republic of China
  • MR Author ID: 1102194
  • Email: ycheng@smail.nju.edu.cn
  • Xiong Meng
  • Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang Province, People’s Republic of China
  • MR Author ID: 998988
  • Email: xiongmeng@hit.edu.cn
  • Qiang Zhang
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, Jiangsu Province, People’s Republic of China
  • MR Author ID: 637183
  • Email: qzh@nju.edu.cn
  • Received by editor(s): June 6, 2015
  • Received by editor(s) in revised form: October 28, 2015
  • Published electronically: September 1, 2016
  • Additional Notes: The research of the first author was supported by NSFC grant 11271187 and the program B for outstanding PhD candidate of Nanjing University.
    The research of the second author was supported by PIRS of HIT grant B201404 and NSFC grant 11501149. Additional support was provided by the EU under the 7th Framework Programme Marie Curie International Incoming Fellowships FP7-PEOPLE-2013-IIF, GA number 622845 while the author was in residence at University of East Anglia, United Kingdom
    The research of the third author was supported by NSFC grants 11271187 and 11571290
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 1233-1267
  • MSC (2010): Primary 65M12, 65M15, 65M60
  • DOI: https://doi.org/10.1090/mcom/3141
  • MathSciNet review: 3614017