Evolving surface finite element methods for random advection-diffusion equations
Provides rigorous numerical analysis for stochastic PDEs on evolving surfaces, a problem relevant to applications in biology and materials science.
The paper develops and analyzes a surface finite element method for advection-diffusion equations with random coefficients on evolving surfaces, proving optimal error bounds for the semi-discrete solution and Monte Carlo estimates of its expectation, validated by 2D and 3D experiments.
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.