Anisotropic Mesh And Finite Element Superconvergence

Mesh generation is the fundamental procedure in finite element simulation. Whenthe solutions change rapidly in one direction, it’s a better choice to choose anisotropictriangulations. Because anisotropy can not only get a better approximation, but greatlyreduce the number of elements, and therefore the computation time. In this thesis, wefocused on the generation of anisotropic triangulations and the superconvergence phe-nomena of the finite element based on such meshes. For the2D elliptic partial difer-ential equation with a symmetric, definite positive constant coefcient matrix, we firstintroduced a metric tensor derived from the coefcient matrix. Then with this metric ten-sor, we used Centroidal Voronoi Tessellation (CVT) algorithm to generate anisotropicCentroidal Voronoi Delaunay Triangulation (ACVDT). The numerical experimental re-sults verified that the relationship between the coefcient matrix and the metric tensorwas reasonable and we found the superconvergence phenomena was not so obvious. Atlast, we analyzed the possible reasons and gave the future study plans.