A High-order Arbitrary Lagrangian-Eulerian Virtual Element Method for Convection-Diffusion Problems
Numerical Analysis
2024-04-30 v1 Numerical Analysis
Abstract
A virtual element discretisation of an Arbitrary Lagrangian-Eulerian method for two-dimensional convection-diffusion equations is proposed employing an isoparametric Virtual Element Method to achieve higher-order convergence rates on curved edged polygonal meshes. The proposed method is validated with numerical experiments in which optimal and convergence are observed. This method is then successfully applied to an existing moving mesh algorithm for implicit moving boundary problems in which higher-order convergence is achieved.
Cite
@article{arxiv.2404.17661,
title = {A High-order Arbitrary Lagrangian-Eulerian Virtual Element Method for Convection-Diffusion Problems},
author = {H. Wells},
journal= {arXiv preprint arXiv:2404.17661},
year = {2024}
}