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A domain mapping approach for elliptic equations posed on random bulk and surface domains

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Church, Lewis, Djurdjevac, Ana and Elliott, Charles M. (2020) A domain mapping approach for elliptic equations posed on random bulk and surface domains. Numerische Mathematik, 146 . pp. 1-49. doi:10.1007/s00211-020-01139-7

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Official URL: http://dx.doi.org/10.1007/s00211-020-01139-7

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Abstract

In this article, we analyse the domain mapping method approach to approximate statistical moments of solutions to linear elliptic partial differential equations posed over random geometries including smooth surfaces and bulk-surface systems. In particular, we present the necessary geometric analysis required by the domain mapping method to reformulate elliptic equations on random surfaces onto a fixed deterministic surface using a prescribed stochastic parametrisation of the random domain. An abstract analysis of a finite element discretisation coupled with a Monte-Carlo sampling is presented for the resulting elliptic equations with random coefficients posed over the fixed curved reference domain and optimal error estimates are derived. The results from the abstract framework are applied to a model elliptic problem on a random surface and a coupled elliptic bulk-surface system and the theoretical convergence rates are confirmed by numerical experiments.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Finite element method , Random fields , Elliptic functions
Journal or Publication Title: Numerische Mathematik
Publisher: Springer
ISSN: 0029-599X
Official Date: September 2020
Dates:
DateEvent
September 2020Published
1 August 2020Available
9 April 2020Accepted
Volume: 146
Page Range: pp. 1-49
DOI: 10.1007/s00211-020-01139-7
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP /HO23364/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
390685689[DFG] Deutsche Forschungsgemeinschafthttp://dx.doi.org/10.13039/501100001659
Wolfson Research Merit AwardRoyal Societyhttp://dx.doi.org/10.13039/501100000288
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