Sobolev方程的各向异性非协调Crouzeix-Raviart型有限元分析

Anisotropic Nonconforming Crouzeix-Raviart Type FEM for Sobolev Equation

在各向异性网格剖分下,将一类Crouzeix-Raviart型非协调线性三角形元应用到Sobolev方程,建立了相应的半离散混合元格式.在抛弃传统有限元分析的必要工具Ritz投影算子的前提下,直接利用剖分单元的插值性质,得到了半离散格式的收敛性分析和最优误差估计,丰富了混合有限元的应用.

In this paper , a Crouzeix-Raviart type nonconforming linear triangular finite element was applied to Sobolev equation on anisotropic mesh and the semi -discrete mixed element formulations were estab-lished respectively .By utilizing the properties of the interpolation on the element instead of the Ritz projection operator, which is an indispensable tool in the traditional finite element analysis , the convergence analysis and optimal error estimations were derived under the discrete formulations , which extends the application of noncon-forming mixed finite element .