各向异性网格下抛物方程一个新的非协调混合元收敛性分析  

CONVERGENCE ANALYSIS OF A NEW NONCONFORMING MIXED FINITE ELEMENT FOR PARABOLIC EQUATION ON ANISOTROPIC MESH

作　　者：张亚东[1] 石东洋[2] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]郑州大学数学系,郑州450052

出　　处：《计算数学》2013年第2期171-180,共10页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10971203;11271340);高等学校博士学科点专项基金(2009410111006)资助项目

摘　　要：本文将Crouzeix-Raviart型非协调线性三角形元应用到抛物方程,建立了一个新的混合元格式.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和导数转移技巧,分别得到了各向异性剖分下关于原始变量u的H^1-模和积分意义下L^2-模以及通量(?)=-▽u在L^2-模下的最优阶误差估计.数值结果与我们的理论分析是相吻合的.In this paper, a Crouzeix-Raviart type nonconforming linear triangular finite element is applied to the parabolic equation and a new mixed element formulation is established. By utilizing the properties of the interpolation on the element and derivative delivery techniques instead of the Ritz projection operator, which is an indispensable tool in the traditional finite element analysis, the optimal order error estimates for the primitive solution u in broken Hi-norm and L2-norm with integral and the flux p=-↓△ in L2-norm are obtained on anisotropic meshes, respectively. The numerical results show the validity of the theoretical analysis.

关 键 词：抛物方程 非协调元 新混合元格式 各向异性网格 收敛性分析 

分 类 号：O241.82[理学—计算数学]