an:01663262
Zbl 1012.76047
Machmoum, A.; Esselaoui, D.
Finite element approximation of viscoelastic fluid flow using characteristics method
EN
Comput. Methods Appl. Mech. Eng. 190, No. 42, 5603-5618 (2001).
00077908
2001
j
76M10 76A10
finite element method; Oldroyd's B model; viscoelastic fluid; extra-stress tensor; upwinding; method of characteristics; fixed point method; error bound
Summary: It is known that for numerical approximation of Oldroyd's B model for viscoelastic fluid flows some upwinding is needed for the convection of extra-stress tensor. In this paper we make numerical analysis of such an approximation with upwinding by the method of characteristics in a finite element context. The approximate stress, velocity, and pressure are, respectively, \(P_1\) discontinuous, \(P_2\) continuous, and \(P_1\) continuous. We suppose that the continuous problem admits a sufficiently smooth and sufficiently small solution. We show by a fixed point method that the approximate problem has a solution, and give an error bound.