Polyhedral Discretizations for Elliptic PDEs

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Constructed a comprehensive mesh dataset by collecting, categorizing and handwriting commonly used polygonal mesh generation and triangulation methods on various domains. Conducted large-scale comparisons of the performance of FEMs and VEMs in terms of solving time for linear systems on solving Poisson and Linear Elasticity problems. The experiment results draw instructive observations in terms of solver categories, PDE selections, mesh quality refinements, and discretization choices.