Evolving surface finite element methods for random advection-diffusion equations

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