Authors: Đurđevac, Ana 
Elliott, Charles
Kornhuber, Ralf
Ranner, Thomas
Title: Evolving surface finite element methods for random advection-diffusion equations
Journal: SIAM-ASA Journal on Uncertainty Quantification
Volume: 6
Issue: 4
First page: 1656
Last page: 1684
Issue Date: 1-Jan-2018
Rank: M22
ISSN: 2166-2525
DOI: 10.1137/17M1149547
Abstract: 
In this paper, we introduce and analyze a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating the unique solvability of the resulting semidiscrete problem, we prove optimal error bounds for the semidiscrete solution and Monte Carlo sampling of its expectation in appropriate Bochner spaces. Our theoretical findings are illustrated by numerical experiments in two and three space dimensions.
Keywords: Random advection-diffusion equation | Surface finite elements | Surface PDEs | Uncertainty quantification
Publisher: Society for Industrial and Applied Mathematics
Project: Engineering and Physical Sciences Research Council (EPSRC EP/J004057/1)
EPSRC programme grant (EP/K034154/1)

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