Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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.

 

The highest order superconvergence for bi-$k$ degree rectangular elements at nodes: A proof of $2k$-conjecture
HTML articles powered by AMS MathViewer

by Chuanmiao Chen and Shufang Hu
Math. Comp. 82 (2013), 1337-1355
DOI: https://doi.org/10.1090/S0025-5718-2012-02653-6
Published electronically: December 5, 2012

Abstract:

We proved the highest order superconvergence $(u-u_h)(z)=O(h^{2k})|\ln h|$ at nodes $z$, based on Element Orthogonality Analysis (EOA), correction techniques and tensor product, where $u\in W^{2k,\infty }(\Omega )$ is the solution for the Poisson equation $-\Delta u=f$ in a rectangle $\Omega$, $u=0$ on $\Gamma$, and $u_h\in S^h_0$ is its bi-$k$ degree rectangular finite element approximation. This conclusion is also verified by numerical experiments for $k=4,5$.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2010): 65N30, 65N15
  • Retrieve articles in all journals with MSC (2010): 65N30, 65N15
Bibliographic Information
  • Chuanmiao Chen
  • Affiliation: College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081 Hunan, People’s Republic of China
  • Email: cmchen@hunnu.edu.cn
  • Shufang Hu
  • Affiliation: College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081 Hunan, People’s Republic of China
  • Email: shufanghu@163.com
  • Received by editor(s): November 23, 2009
  • Received by editor(s) in revised form: November 1, 2010, June 21, 2011, September 26, 2011, October 3, 2011, and November 22, 2011
  • Published electronically: December 5, 2012
  • Additional Notes: The first author was supported by The National Natural Science Foundation of China (No. 10771063), Key Laboratory of High Performance Computation and Stochastic Information Processing, Hunan Province and Ministry of Education, Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province, and The Graduate Student Research Innovation Foundation of Hunan (No. CX2011B184)
  • © Copyright 2012 American Mathematical Society
  • Journal: Math. Comp. 82 (2013), 1337-1355
  • MSC (2010): Primary 65N30, 65N15
  • DOI: https://doi.org/10.1090/S0025-5718-2012-02653-6
  • MathSciNet review: 3042566