CAJ | 학술논문

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.
채용은정화유한원법대복종Oldroyd B형구성률적점탄성류동수치분석.응력,속도화압력분별용불련속분편k차다항식Pk,련속분편k+1차다항식Pk+1화련속분편k차다항식Pk핍근,저리k≥0위임의정수.Lesaint-Raviart방법피용우처리부가응력장량적확대류항.재가설련속문제유일충분소적광활해적정황하,용불동점정리증명료핍근문제유유일해,병급출료오차고계.
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.