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Robust nonconforming virtual element methods for general fourth order problems with varying coefficients

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Dedner, Andreas and Hodson, Alice (2021) Robust nonconforming virtual element methods for general fourth order problems with varying coefficients. IMA Journal of Numerical Analysis . drab003. doi:10.1093/imanum/drab003 ISSN 0272-4979.

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Official URL: https://doi.org/10.1093/imanum/drab003

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Abstract

We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element spaces. Optimal error estimates in the energy norm are provided for general linear fourth order problems with varying coefficients. We also discuss fourth order perturbation problems and present a novel nonconforming scheme which is uniformly convergent with respect to the perturbation parameter without requiring an enlargement of the space. Numerical tests are carried out to verify the theoretical results. We conclude with a brief discussion on how our approach can easily be applied to nonlinear fourth order problems.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Differential equations, Partial, Finite element method
Journal or Publication Title: IMA Journal of Numerical Analysis
Publisher: Oxford University Press
ISSN: 0272-4979
Official Date: 17 March 2021
Dates:
DateEvent
17 March 2021Published
8 January 2021Accepted
Article Number: drab003
DOI: 10.1093/imanum/drab003
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): This is a pre-copyedited, author-produced version of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record Andreas Dedner, Alice Hodson, Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients, IMA Journal of Numerical Analysis, 2021;, drab003, is available online at: https://doi.org/10.1093/imanum/drab003
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 9 February 2021
Date of first compliant Open Access: 17 March 2022
Open Access Version:
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