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Second order splitting for a class of fourth order equations
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Elliott, Charles M., Fritz, Hans and Hobbs, Graham (2019) Second order splitting for a class of fourth order equations. Mathematics of Computation, 88 . pp. 2605-2634. doi:10.1090/mcom/3425 ISSN 0025-5718.
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WRAP-second-order-splitting-class-fourth-order-equations-Elliot-2018.pdf - Accepted Version - Requires a PDF viewer. Download (739Kb) | Preview |
Official URL: https://doi.org/10.1090/mcom/3425
Abstract
We formulate a well-posedness and approximation theory for a class of generalised saddle point problems. In this way we develop an approach to a class of fourth order elliptic partial differential equations using the idea of splitting into coupled second order equations. Our main motivation is to treat certain fourth order equations on closed surfaces arising in the modelling of biomembranes but the approach may be applied more generally. In particular we are interested in equations with non-smooth right-hand sides and operators which have non-trivial kernels. The theory for well-posedness and approximation is presented in an abstract setting. Several examples are described together with some numerical experiments.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Approximation theory, Method of steepest descent (Numerical analysis) , Differential equations, Elliptic | ||||||
| Journal or Publication Title: | Mathematics of Computation | ||||||
| Publisher: | American Mathematical Society | ||||||
| ISSN: | 0025-5718 | ||||||
| Official Date: | 1 April 2019 | ||||||
| Dates: |
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| Volume: | 88 | ||||||
| Page Range: | pp. 2605-2634 | ||||||
| DOI: | 10.1090/mcom/3425 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | First published in Mathematics of Computation in [volume/issue number and year], published by the American Mathematical Society | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | © Copyright 2019 American Mathematical Society | ||||||
| Date of first compliant deposit: | 13 February 2019 | ||||||
| Date of first compliant Open Access: | 9 April 2019 |
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