353
Views
29
CrossRef citations to date
0
Altmetric
Original Article

Virtual element method for semilinear hyperbolic problems on polygonal meshes

, &
Pages 971-991 | Received 26 Oct 2017, Accepted 30 Apr 2018, Published online: 01 Jun 2018
 

ABSTRACT

This article deals with the development of the virtual element method for the approximation of semilinear hyperbolic problems. For the space discretization, two different operators are used: the energy projection operator Πk,K and an internal L2-projection operator Πk,K0. In order to deal with the time derivative, a Newmark scheme is employed; and the resulted fully discrete scheme is analysed. Moreover, with the help of projection operators, optimal error estimates are derived for both semi- and fully discrete schemes in L2-norm and H1-norm. We have conducted numerical experiments on polygonal meshes to illustrate the performance of the proposed scheme and validate the theoretical findings.

2010 AMS SUBJECT CLASSIFICATIONS:

Disclosure statement

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

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 1,129.00 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.