中文摘要：

对Sobolev方程采用混合有限元法进行数值模拟,给出了相应的半离散格式及其误差估计,构造了几组简单的低阶元.与已有文献中的有限元方法相比,该方法所采用的变分形式较简单,计算量较小,精度较高.通过对单元刚度矩阵的分析,得出在一维和二维情形下通量函数选取某些不同模式得到的关于位移的单元刚度矩阵等同.

英文摘要：

By introducing the mixed finite element method for Sobolev equation, the corresponding semi-discrete formulation is presented and the error estimates are obtained, and a series of lower-order elements are constructed, Compared to the known finite element methods, this method takes simpler variational formulationm, costs less computation and has higher accuracy . Through analyzing element stiffness matrix, it can be derived that the element stiffness matrixes with displacements are equivalent when flux function selects some different modes in one and two dimension.