中文摘要：

文中研究非Newton（牛顿）流体流变问题的混合型双曲抛物一阶偏微分方程的收敛性，采用耦合的偏微分方程组（Cauchy流体方程、P—T／T应力方程），模拟自由表面元或由过度拉伸元素产生的流域．使用半离散有限元方法进行求解，对于含有时间变量的耦合方程，在空间上用有限元法，利用三线性泛函来解决偏微分方程组的非线性；在时间上用Euler（欧拉）格式，得出方程组的收敛精度可达到0（h2＋△t）．通过高性能计算的预估计和后估计得到方程的数值结果，并显示网格变形的大小．

英文摘要：

Convergence of the first-order mixed-type hyperbolic parabola partial differential e- quations in non-Newtonian fluid problems was studied. The coupling partial differential equa- tions （Cauchy fluid equation, P-T/T stress equation） were used to simulate the flow zone gen- erated by the free surface elements or excessively tensile elements. The semi-discrete finite ele- ment method was applied to solve these equations coupling with time. The finite element meth- od was used in space. The trilinear functional was employed to solve the nonlinear problems of partial differential equations. In the time domain the Euler scheme was adopted. The conver- gence order of the equation set reached O（ h2 ＋ At） . Numerical results of the equations were ob- tained through priori and posteriori error estimation of high performance computation. And the deformed sizes of the grids were presented.