Stabilized finite element method for the approximation of linearized viscoelastic fluid flow models
Keywords:
linearized viscoelastic flow, DG method, lowest order pairs, Stabilized method.Abstract
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.
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