Superconvergence Of The Tensor-Product Finite Element In 4D

For the Poisson equation and variable coefficients elliptic equations, weak estimates for the four-dimensional tensor-product finite element over regular partitions of the domain are established for the interpolation operator of projection type. Furthermore, using estimates for the four-dimensional discrete Green’s function, we obtain supercloseness results.This thesis is divided into five sections:Section 1: Introduction.Section 2: We introdue the definitions and estimates of four-dimensional discrete Green’s function and discrete derivative Green’s function, which are elementary means to study the maximum-norm superapproximations of finite elements.Section 3: We introdue the theory of the four-dimensional interpolation operator of projection type, which is an important means to derive weak estimates for finite elements.Section 4: For Dirichlet boundary value problems of Poissonequation We discuss the superconvergence of the four-dimensional tensor-product finite elements.Section 5: For variable coefficients elliptic boundary value problemWe discuss the superconvergence of four-dimensional tensor-product finite elements.