Sandri, Dominique Approximation par éléments finis d’écoulements de fluides viscoélastiques: Existence de solutions approchées et majoration d’erreur. II: Constraintes continues. (Finite element approximation of viscoelastic fluid flow: Existence of approximate solutions and error bounds. II: Continuous constraints). (French) Zbl 0737.76048 C. R. Acad. Sci., Paris, Sér. I 313, No. 2, 111-114 (1991). Summary: [For part I, see: J. Baranger and the author, ibid. 312, No. 7, 541-544 (1991; Zbl 0718.76010).]We study a finite element approximation of viscoelastic fluid flow obeying an Oldroyd B type constitutive law. The approximate stress, velocity and pressure are respectively \(P_ 1\) continuous, \(P_ 2\) continuous, \(P_ 1\) continuous. We use a method of Petrov-Galerkin type for the convection of the extra stress tensor. 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 we give an error bound. Cited in 4 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76A10 Viscoelastic fluids 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:finite element approximation; viscoelastic fluid; Oldroyd B type constitutive law; method of Petrov-Galerkin type Citations:Zbl 0718.76010 PDFBibTeX XMLCite \textit{D. Sandri}, C. R. Acad. Sci., Paris, Sér. I 313, No. 2, 111--114 (1991; Zbl 0737.76048)