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Second order splitting of a class of fourth order PDEs with point constraints
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Elliott, Charles M. and Herbert, P. J. (2020) Second order splitting of a class of fourth order PDEs with point constraints. Mathematics of Computation, 89 . pp. 2613-2648. doi:10.1090/mcom/3556 ISSN 0025-5718.
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Official URL: https://doi.org/10.1090/mcom/3556
Abstract
We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential equations with point constraints using the idea of splitting into coupled second order equations. An approach is formulated using a penalty method to impose the constraints. Our main motivation is to treat certain fourth order equations involving the biharmonic operator and point Dirichlet constraints for example arising in the modelling of biomembranes on curved and flat surfaces but the approach may be applied more generally. 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 | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Approximation theory, Differential equations, Elliptic, Biholomorphic mappings, Dirichlet forms | |||||||||
Journal or Publication Title: | Mathematics of Computation | |||||||||
Publisher: | American Mathematical Society | |||||||||
ISSN: | 0025-5718 | |||||||||
Official Date: | 27 July 2020 | |||||||||
Dates: |
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Volume: | 89 | |||||||||
Page Range: | pp. 2613-2648 | |||||||||
DOI: | 10.1090/mcom/3556 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Reuse Statement (publisher, data, author rights): | “First published in Mathematics of Computation in 89, 2020 published by the American Mathematical Society,” and the copyright notice in proper form must be placed on all copies. | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Copyright Holders: | © Copyright 2020, American Mathematical Society | |||||||||
Date of first compliant deposit: | 5 May 2020 | |||||||||
Date of first compliant Open Access: | 5 May 2020 | |||||||||
RIOXX Funder/Project Grant: |
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