A convergent three field quadrilateral finite element method for simulating viscoelastic flow on irregular meshes. (English) Zbl 0924.76060

Summary: In a recent paper [D. Sandri, Thèse, Lyon (1991)] a finite element method for solving the three field Stokes system as a basis for the numerical solution of viscoelastic fluid flow problems was introduced. The method constructed upon a biquadratic velocity, a discontinuous linear pressure and a bilinear extra stress tensor interpolation in quadrilaterals, enriched with fifteen bubble tensors, has been proved to yield second order approximations of these variables, in the case of rectangular meshes. In this work equivalent results are proven to hold in the case of irregular meshes.


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
35Q30 Navier-Stokes equations
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