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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

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Official URL: https://doi.org/10.1090/mcom/3425

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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 > 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:
DateEvent
1 April 2019Published
11 January 2019Accepted
Volume: 88
Page Range: pp. 2605-2634
DOI: 10.1090/mcom/3425
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: 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

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