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arXiv · 2404.17661

A High-order Arbitrary Lagrangian-Eulerian Virtual Element Method for Convection-Diffusion Problems

H. Wells
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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 $H^1$ and $L^2$ 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.

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H. Wells. 2024-04-26. A High-order Arbitrary Lagrangian-Eulerian Virtual Element Method for Convection-Diffusion Problems. https://arxiv.org/abs/2404.17661

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