Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow

We consider the application of Fictitious Domain approach combined with least squares spectral elements for the numerical solution of fluid dynamic incompressible equations. Fictitious Domain methods allow problems formulated on a complicated shaped domain Ω$\Omega$ to be solved on a simpler domain Π$\Pi$ containing Ω$\Omega$. Least Squares Spectral Element Method has been used to develop the discrete model, as this scheme combines the generality of finite element methods with the accuracy of spectral methods. Moreover the least squares methods have theoretical and computational advantages in the algorithmic design and implementation. This paper presents the formulation and validation of the Fictitious Domain Least Squares Spectral Element approach for the steady incompressible Navier–Stokes equations. The convergence of the approximated solution is verified solving two-dimensional benchmark problems, demonstrating the predictive capability of the proposed formulation.