The Library
A domain mapping approach for elliptic equations posed on random bulk and surface domains
Tools
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 ISSN 0029-599X.
|
PDF
WRAP-domain-mapping-elliptic-equations-random-surface-Elliott-2020.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (767Kb) | Preview |
Official URL: http://dx.doi.org/10.1007/s00211-020-01139-7
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, Engineering and Medicine > 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: |
|
||||||||||||
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 (Creative Commons) | ||||||||||||
Date of first compliant deposit: | 4 August 2020 | ||||||||||||
Date of first compliant Open Access: | 4 August 2020 | ||||||||||||
RIOXX Funder/Project Grant: |
|
||||||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year