Abstract
In this article, a stabilized mixed finite element (FE) method for the Oseen viscoelastic fluid flow (OVFF) obeying an Oldroyd-B type constitutive law is proposed and investigated by using the Streamline Upwind Petrov–Galerkin (SUPG) method. To find the approximate solution of velocity, pressure and stress tensor, we choose lowest-equal order FE triples P 1 - P 1 - P 1 , respectively. However, it is well known that these elements do not fulfill the i n f - s u p condition. Due to the violation of the main stability condition for mixed FE method, the system becomes unstable. To overcome this difficulty, a standard stabilization term is added in finite element variational formulation. The technique is applied herein possesses attractive features, such as parameter-free, flexible in computation and does not require any higher-order derivatives. The stability analysis and optimal error estimates are obtained. Three benchmark numerical tests are carried out to assess the stability and accuracy of the stabilized lowest-equal order feature of the OVFF.
Highlights
The research interest in viscoelastic fluids has increased, due to the connections with industrial applications
The steady-state (Johnson–Segalman) model equations can be seen in different viscoelastic articles; for the extensive theoretical modeling and numerical analysis for the considered model, we refer to [9,10,19,23] and the references therein
We studied an approximation of the Oseen viscoelastic fluid flow (OVFF)
Summary
The research interest in viscoelastic fluids has increased, due to the connections with industrial applications. A standard pressure term (stabilized) is added with the incompressibility condition in order to cure the classical in f -sup condition between the velocity and the pressure spaces (as in the Stokes equations), and the SUPG scheme is employed in order to treat the hyperbolic nature of viscoelastic constitutive equations. In this context, there is no specific analysis available yet to approximation the OVFF by using the lowest-equal order triples.
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