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中文摘要：
利用积分恒等式和插值后处理技术,本文在各向异性网格上对Sobolev型方程的Carey非协调有限元解进行高精度算法分析。首先,根据Carey元的特性,即其有限元解的线性插值和线性元解相同,我们构造插值后处理算子,得到了有限元解的超逼近性质和整体超收敛及后验误差估计。接着,根据误差渐近展开式,运用外推方法,进一步得到了具有四阶精度的近似解。
英文摘要：
By using the integral identities and the interpolation postprocessing technique, the higher accuracy approximation of the anisotropic nonconforming Carey element for solving the Sobolev type equations is investigated. Firstly, the interpolation operator is constructed, the superclose~ global superconvergence and posteriori error estimate are obtained with the help of the distinct property of Carey elements, i.e., the linear interpolation of the solution for Carey elements is equal to the solution for linear triangular element. Secondly, by virtue of the extrapolation method, the accuracy of the related approximate solution with fourth order is derived through the asymptotic error expansion.
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