Stabilized finite element method for the approximation of linearized viscoelastic fluid flow models

Shahid Hussain, Zahid Hussain, Sajid Hussain, Vishnu Narayan Mishra


In this article, we present a stabilized finite element (FE)
method for the linearized viscoelastic fluid flow. The FE spaces for the
unknown variables are chosen as P 1-P 0-P 1, where the fluid velocity
and the pressure are discretized by the lowest-order Lagrange elements
and the stress tensor is discretized by piecewise P 1 polynomial. In order
to get a stable scheme, we added a stabilization term. This method has
some prominent features: parameter-free, avoiding calculation of higherorder derivatives and its behaviour towards pressure is totally local.
We obtained optimal error estimates and presented several numerical
experiments to verify the proposed scheme.


linearized viscoelastic flow; DG method; lowest order pairs; Stabilized method.


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