黏弹性流动数值模拟的稳定化方法

采用稳定化有限元法对服从Oldroyd B型构成律的黏弹性流动数值分析。应力，速度和压力分别用不连续分片k次多项式Pk，连续分片k 1次多项式Pk 1和连续分片k次多项式Pk逼近，这里k≥0为任意整数。Lesaint-Raviart方法被用于处理附加应力张量的扩对流项。在假设连续问题有一充分小的光滑解的情况下，用不动点定理证明了逼近问题有唯一解，并给出了误差估计。

A Stabilized Finite Element Approximation of Viscoelastic Fluid Flow

The authors devoted to the numerical analysis of a stabilized finite element approxima-tion for viscoelastic fluid flow obeying an Oldroyd B type constitutive law. The approximatestress, velocity and pressure are respectively Pk discontinuous, Pk+1 continuous and Pk continuousfor an arbitrary integer k ≥ 0. The method of Lesaint-Raviart for the convection of the extrastress tensor is used. When asuming the continuous problem admits a sufficiently smooth and suf-ficiently small solution, the approximate problem is proved to have a unique solution by employinga fixed point method, and an error estimate is derived.