Evolving surface finite element methods for random advection-diffusion equations
Numerical Analysis
2017-09-26 v2
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.
Cite
@article{arxiv.1702.07290,
title = {Evolving surface finite element methods for random advection-diffusion equations},
author = {Ana Djurdjevac and Charles M. Elliott and Ralf Kornhuber and Thomas Ranner},
journal= {arXiv preprint arXiv:1702.07290},
year = {2017}
}