Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 6
90
Views
1
CrossRef citations to date
0
Altmetric
Articles

Superconvergence analysis for a semilinear parabolic equation with BDF-3 finite element method

Pages 1822-1832 | Received 13 Dec 2018, Accepted 16 Jun 2020, Published online: 08 Jul 2020
 

ABSTRACT

The main aim of this paper is to obtain superconvergence result for a semilinear parabolic equation with 3-step backward differential formula Galerkin finite element method. The time-discrete system is established to split the error into the temporal error and spatial error. The initial two steps of the temporal error is dealt with by a new way to ensure the third-order accuracy of the scheme. Some new tricks are utilized to get the spatial error in H1-norm of order O(h(h+τ32)) without the ratio between the spatial subdivision parameter h and the temporal step τ, which improves the corresponding results in the previous literature. The final superconvergence result is deduced by the above achievements and trigonometric inequality. Two numerical examples are provided to support the theoretical analysis.

COMMUNICATED BY:

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11671369) and Pingdingshan University High-level Talents Start-up Fund (PXY-BSQD-2019001).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [No. 11671369] and Pingdingshan University High-level Talents Start-up Fund [PXY-BSQD-2019001].

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,361.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.