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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
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Official URL: https://doi.org/10.1093/imanum/drab003
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 | ||||||
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| 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: |
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| 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 | ||||||
| Open Access Version: |
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