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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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WRAP-evolving-surface-finite-element-methods-random-advection-diffusion-equations-Elliot-2018.pdf - Accepted Version - Requires a PDF viewer. Download (955Kb) | Preview |
Official URL: https://doi.org/10.1137/17M1149547
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 | ||||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QD Chemistry |
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| 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 | ||||||||||||
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| 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 | ||||||||||||
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