双调和方程的非协调扩展混合元方法的高精度分析

High Accuracy Analysis of an Expanded Nonconforming Mixed Finite Elements Method for the Biharmonic Equation

借助于EQ_1^(rot)元及零阶Raviart-Thomas(R-T)元对双调和方程提出了非协调扩展混合有限元格式,利用EQ_1^(rot)元已有的2个特殊性质及零阶R-T元的高精度技巧,导出了相关变量的超逼近结果.进一步,通过构造一个新的外推格式,得到了具有O(h^3)的外推解,其中h表示空间剖分参数.

Based on the EQ1^rot and the zero order Raviart-Thomas elements,an expanded nonconforming mixed finite elements approximation scheme is proposed for the biharmonic equation.By using the two special properties of EQ1^rot elements and known high accuracy analysis of zero R-T elements,the superclose properties of the related variables are derived.Further,through constructing a suitable extrapolation scheme,the extrapolation solutions with order O（h^3）are obtained.Here,his the subdivision parameter for the space.