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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 H1H^1 and L2L^2 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.

Keywords

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}
}
R2 v1 2026-06-28T16:08:08.464Z