Second order splitting for a class of fourth order equations
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- by Charles M. Elliott, Hans Fritz and Graham Hobbs HTML | PDF
- Math. Comp. 88 (2019), 2605-2634 Request permission
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.References
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Additional Information
- Charles M. Elliott
- Affiliation: Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, United Kingdom
- MR Author ID: 62960
- ORCID: 0000-0002-6924-4455
- Email: C.M.Elliott@warwick.ac.uk
- Hans Fritz
- Affiliation: Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
- MR Author ID: 1106591
- Email: fritz.hans@web.de
- Graham Hobbs
- Affiliation: Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, United Kingdom
- MR Author ID: 1176722
- Email: graham.hobbs@warwickgrad.net
- Received by editor(s): November 11, 2017
- Received by editor(s) in revised form: October 5, 2018, and December 16, 2018
- Published electronically: April 1, 2019
- Additional Notes: The work of the first author was partially supported by the Royal Society via a Wolfson Research Merit Award.
The second author thanks the Alexander von Humboldt Foundation, Germany, for their financial support by a Feodor Lynen Research Fellowship in collaboration with the University of Warwick, UK
The research of the third author was funded by the Engineering and Physical Sciences Research Council grant EP/H023364/1 under the MASDOC centre for doctoral training at the University of Warwick. - © Copyright 2019 American Mathematical Society
- Journal: Math. Comp. 88 (2019), 2605-2634
- MSC (2010): Primary 65N30, 65J10, 35J35
- DOI: https://doi.org/10.1090/mcom/3425
- MathSciNet review: 3985470