dc.contributor.author
Djurdjevac, Ana
dc.date.accessioned
2018-12-19T13:50:32Z
dc.date.available
2018-12-19T13:50:32Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/23623
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-1408
dc.description.abstract
Partial differential equations with random coefficients (random PDEs) is a
very developed and popular field. The variety of applications, especially in biology, motivate us to consider the random PDEs on curved moving domains. We introduce and analyse the advection-diffusion equations with random coefficients on moving hypersurfaces. We consider both cases, uniform and log-normal distributions of coefficients. Furthermore, we will introduce and analyse a surface finite element discretisation of the equation. We show unique solvability of the resulting semi-discrete problem and prove optimal error bounds for the semi-discrete solution and Monte Carlo samplings of its expectation.
Our theoretical findings are illustrated by numerical experiments. In the end
we present an outlook for the case when the velocity of a hypersurface is
an uniformly bounded random field and the domain is flat.
en
dc.format.extent
xi, 145 Seiten
dc.rights.uri
http://www.fu-berlin.de/sites/refubium/rechtliches/Nutzungsbedingungen
dc.subject
surface partial differential equations
en
dc.subject
uncertainty quantification
en
dc.subject
partial differential equations
en
dc.subject.ddc
500 Natural sciences and mathematics::510 Mathematics::518 Numerical analysis
dc.subject.ddc
500 Natural sciences and mathematics::510 Mathematics::515 Analysis
dc.title
Random partial differential equations on evolving hypersurfaces
dc.contributor.gender
female
dc.contributor.firstReferee
Kornhuber, Ralf
dc.contributor.furtherReferee
Elliott, Charles
dc.date.accepted
2018-11-27
dc.identifier.urn
urn:nbn:de:kobv:188-refubium-23623-7
refubium.affiliation
Mathematik und Informatik
dcterms.accessRights.dnb
free
dcterms.accessRights.openaire
open access
dcterms.accessRights.proquest
accept