Maxwell方程的各向异性MECHL元的高精度分析

主要研究在各向异性网格下MECHL元对Maxwell方程的应用.通过证明一个新的引理,结合该单元已有的高精度估计,给出相应的向后Euler全离散格式以及Crank-Nicolson-Galerkin全离散格式的超逼近和超收敛的结果.同时,通过算例验证了理论分析的正确性.该结果进一步说明传统有限元分析中要求的剖分满足正则性条件是不必要的,从而克服了以往文献的不足.

Superconvergence Analysis of MECHL Finite Element for Maxwell's Equation on Anisotropic Meshes

The application of MECHL finite element to Maxwell' s equation on anisotropic meshes is mainly investigated. By proving a new lemma together with the known high accuracy estimates of this element, the superclose and superconvergence results of the backward Euler and Crank-Nicolson-Galerkin fully discrete schemes are given. At the same time, a numerical example is provided to verify the theoretical analysis. The results further show that the regularity condition on the subdivision in traditional finite element analysis is not necessary, and thus the defects of the previous literature are overcomed.