2024/04/26 by Wells, H.
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2404.17661
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.