拟线性双曲积分微分方程的一个新混合元分析

Analysis of a New Nonconforming Mixed Finite Element for Quasilinear Hyperbolic Type Integro-differential Equations

利用协调线性三角形元对一类拟线性双曲积分微分方程建立了一个新的混合元格式.在抛弃传统有限元分析中的Ritz投影的前提下,直接利用单元上的插值算子的性质,平均值及导数转移技巧,给出了相应的H^1-模及L^2-模最优误差估计.同时借助于高精度和插值后处理技巧,导出了相应的超逼近及超收敛结果.

Using coordinated linear triangular element for a class of quasilinear hyperbolic integro differential equations, the papaer establishes a new mixed element formulation. On the premise of abandoning the conven-tional Ritz projection in finite element analysis , directly on the properties of the interpolation operator unit, aver-age value and derivative transfer techniques, the corresponding optimal error estimates in H1-norm and in L2- norm are obtained. At the same time, based on high accuracy and interpolation -post processing techniques, the corresponding superclose and superconvergence results are obtained.