Elliott, CM and Ranner, T orcid.org/0000-0001-7682-3175 (2021) A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains. IMA Journal of Numerical Analysis, 41 (3). draa062. pp. 1696-1845. ISSN 0272-4979
Abstract
We develop a unified theory for continuous-in-time finite element discretizations of partial differential equations posed in evolving domains, including the consideration of equations posed on evolving surfaces and bulk domains, as well as coupled surface bulk systems. We use an abstract variational setting with time-dependent function spaces and abstract time-dependent finite element spaces. Optimal a priori bounds are shown under usual assumptions on perturbations of bilinear forms and approximation properties of the abstract finite element spaces. The abstract theory is applied to evolving finite elements in both flat and curved spaces. Evolving bulk and surface isoparametric finite element spaces defined on evolving triangulations are defined and developed. These spaces are used to define approximations to parabolic equations in general domains for which the abstract theory is shown to apply. Numerical experiments are described, which confirm the rates of convergence.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2020. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is an author produced version of an article published in . Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | abstract error analysis; advection–diffusion on evolving surfaces; bulk-surface parabolic equations; evolving bulk finite element methods; evolving finite element spaces; evolving surface finite element methods; parabolic equations on moving domains |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number Leverhulme Trust ECF-2017-591 |
Depositing User: | Symplectic Publications |
Date Deposited: | 02 Dec 2020 14:14 |
Last Modified: | 21 Nov 2023 10:55 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/imanum/draa062 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:120238 |