Evolving surface finite element methods for random advection-diffusion equations

Abstract

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 semi-discrete 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.

References in corpus (3)

• An abstract framework for parabolic PDEs on evolving spaces
• Numerical analysis of lognormal diffusions on the sphere
• Quasi-optimality of Petrov-Galerkin discretizations of parabolic problems with random coefficients