Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Superconvergence of Local Discontinuous Galerkin methods for one-dimensional linear parabolic equations
HTML articles powered by AMS MathViewer

by Waixiang Cao and Zhimin Zhang PDF
Math. Comp. 85 (2016), 63-84 Request permission

Abstract:

In this paper, we study superconvergence properties of the local discontinuous Galerkin method for one-dimensional linear parabolic equations when alternating fluxes are used. We prove, for any polynomial degree $k$, that the numerical fluxes converge at a rate of $2k+1$ (or $2k+1/2$) for all mesh nodes and the domain average under some suitable initial discretization. We further prove a $k+1$th superconvergence rate for the derivative approximation and a $k+2$th superconvergence rate for the function value approximation at the Radau points. Numerical experiments demonstrate that in most cases, our error estimates are optimal, i.e., the error bounds are sharp.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2010): 65M15, 65M60, 65N30
  • Retrieve articles in all journals with MSC (2010): 65M15, 65M60, 65N30
Additional Information
  • Waixiang Cao
  • Affiliation: Beijing Computational Science Research Center, Beijing, 100084, China β€” and β€” College of Mathematics and Computational Science and Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, 510275, China
  • Zhimin Zhang
  • Affiliation: Beijing Computational Science Research Center, Beijing, 100084, China β€” and β€” Department of Mathematics, Wayne State University, Detroit, Michigan 48202
  • Received by editor(s): February 12, 2014
  • Received by editor(s) in revised form: May 10, 2014
  • Published electronically: June 1, 2015
  • Additional Notes: The second author was supported in part by the National Natural Science Foundation of China (NSFC) under grant Nos. 11471031, 91430216, and the US National Science Foundation (NSF) through grant DMS-1419040
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 63-84
  • MSC (2010): Primary 65M15, 65M60, 65N30
  • DOI: https://doi.org/10.1090/mcom/2975
  • MathSciNet review: 3404443