Evolving surface finite element methods for random advection-diffusion equations

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