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 H¹ and L² 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. Gideon Wells (2024) studied this question.
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