抛物型方程一个新的非协调混合元超收敛性分析及外推  

SUPERCONVERGENCE AND EXTRAPOLATION ANALYSIS OF A NEW NONCONFORMING MIXED FINITE ELEMENT APPROXIMATION FOR PARABOLIC EQUATION

作　　者：石东洋[1] 张亚东[2] 

机构地区：[1]郑州大学数学与统计学院,郑州450001 [2]许昌学院数学与统计学院,河南许昌461000

出　　处：《计算数学》2013年第4期337-352,共16页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10971203;11271340;11101381);高等学校博士学科点专项基金(2009410111006);河南省高等学校青年骨干教师资助项目(2011GGJS-182)

摘　　要：本文研究了抛物型方程在新混合元格式下的非协调混合有限元方法.在抛弃传统有限元分析的必要工具-Ritz投影算子的前提下,直接利用单元的插值性质,运用高精度分析和对时间t的导数转移技巧,借助于插值后处理技术,分别导出了关于原始变量u的H^1-模和通量(?)=-▽u在L^2-模下的O(h^2)阶超逼近性质和整体超收敛.进一步,通过构造合适的辅助问题,运用Richardson外推格式,得到了具有更高精度O(h^3)阶的外推结果.最后,给出了一些数值结果验证了理论分析的正确性.In this paper, a new nonconforming mixed finite element method for parabolic equa- tion is studied based on a new mixed variational form. By utilizing the properties of the interpolation on the element, high accuracy analysis and derivative delivery techniques with respect to time t instead of the Ritz projection operator, which is am indispensable tool in the traditional finite element analysis, the superclose properties and the global superconvergence with order O（h2） for the primitive solution u in broken Hi-norm and the flux p=- u in L2-norm are obtained through interpolated postprocessing approach, respectively. Furthermore, by constructing a suitable auxiliary problem, the extrapolation results with higher order O（h3） for u and gare derived through Richardson extrapolation scheme. At last, some numerical results are provided to show the validity of the theoretical analysis.

关 键 词：抛物型方程 非协调元 新混合元格式 超收敛 外推 

分 类 号：O241.82[理学—计算数学]