非线形粘弹性流体的稳定化有限元方法研究

Stabilized Finite Element Method for the Viseoelastic Fluid Flow

对遵循OldroydB型粘弹性动问题 ,提出了一种基于流线迎风Petrow Galerkin方法和最小二乘法相结合的稳定化有限元方法 .这种方法有效地解决了以往粘弹性流体研究过程中出现的由于应力方程对流控制占优引起的拟振动现象和有限元空间组合不匹配产生的不稳定现象 .近似应力 ,速度和压力分别是Pk 连续的 ,Pk+ 1和Pk 的 (k≥ 0 ) .假定连续问题满足充分光滑且小的解 。

The authors give a stabilized finite element method for viscoelastic fluid flow based on SUPG method and least square method. The approximate stress,velocity and pressure are respectively P k continuous, P k+1 and P k. The SUPG method is used for convection of the extra stress tensor; the least square method is used for the combination of the velocity and pressure spaces. When assuming the continuous problem admits a sufficiently smooth and suffciently small solution, the approximate problem is proved to have a unique solution, and an error bound is given.