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.

 

Delay-dependent elliptic reconstruction and optimal $L^\infty (L^2)$ a posteriori error estimates for fully discrete delay parabolic problems
HTML articles powered by AMS MathViewer

by Wansheng Wang and Lijun Yi HTML | PDF
Math. Comp. 91 (2022), 2609-2643 Request permission

Abstract:

We derive optimal order a posteriori error estimates for fully discrete approximations of linear parabolic delay differential equations (PDDEs), in the $L^\infty (L^2)$-norm. For the discretization in time we use Backward Euler and Crank-Nicolson methods, while for the space discretization we use standard conforming finite element methods. A novel space-time reconstruction operator is introduced, which is a generalization of the elliptic reconstruction operator, and we call it as delay-dependent elliptic reconstruction operator. The related a posteriori error estimates for the delay-dependent elliptic reconstruction play key roles in deriving optimal order a posteriori error estimates in the $L^\infty (L^2)$-norm. Numerical experiments verify and complement our theoretical results.
References
Similar Articles
Additional Information
  • Wansheng Wang
  • Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai 200234, People’s Republic of China
  • ORCID: 0000-0002-2128-7501
  • Email: w.s.wang@163.com
  • Lijun Yi
  • Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai 200234, People’s Republic of China
  • MR Author ID: 883098
  • ORCID: 0000-0002-2922-5508
  • Email: ylj5152@shnu.edu.cn
  • Received by editor(s): January 1, 2021
  • Received by editor(s) in revised form: October 19, 2021
  • Published electronically: July 29, 2022
  • Additional Notes: The first author was supported by the Natural Science Foundation of China (Grant No. 11771060), Shanghai Science and Technology Planning Projects (Grant No. 20JC1414200), and Natural Science Foundation of Shanghai (Grant No. 20ZR1441200). The second author was supported by the National Natural Science Foundation of China (Grant Nos. 12171322 and 11771298) and the Natural Science Foundation of Shanghai (Grant No. 21ZR1447200).
    The first author is the corresponding author.
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 2609-2643
  • MSC (2020): Primary 65M12, 65M15, 65L06, 65M60, 65N30; Secondary 65M50, 65L70, 65L50
  • DOI: https://doi.org/10.1090/mcom/3761
  • MathSciNet review: 4473098