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Evolving surface finite element methods for random advection-diffusion equations

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Djurdjevac, Ana, Elliott, Charles M., Kornhuber, Ralf and Ranner, Thomas (2018) Evolving surface finite element methods for random advection-diffusion equations. SIAM/ASA Journal on Uncertainty Quantification, 6 (4). pp. 1656-1684. doi:10.1137/17M1149547

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Official URL: https://doi.org/10.1137/17M1149547

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Abstract

In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating unique solvability of the resulting semidiscrete problem, we prove optimal error bounds for the semi-discrete solution and Monte-Carlo samplings of its expectation in appropriate Bochner spaces. Our theoretical findings are illustrated by numerical experiments in two and three space dimensions.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QD Chemistry
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Finite element method, Hypersurfaces, Diffusion
Journal or Publication Title: SIAM/ASA Journal on Uncertainty Quantification
Publisher: SIAM
ISSN: 2166-2525
Official Date: 20 November 2018
Dates:
DateEvent
20 November 2018Published
10 December 2018Available
17 September 2018Accepted
Volume: 6
Number: 4
Page Range: pp. 1656-1684
DOI: 10.1137/17M1149547
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: Published in SIAM/ASA Journal on Uncertainty Quantification in [volume and number, or year], published by the Society for Industrial and Applied Mathematics (SIAM) Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/J004057/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
Wolfson Research Merit Award[RS] Royal Societyhttp://dx.doi.org/10.13039/501100000288
EP/K034154/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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