A comparative study of different GLS elements for solving incompressible viscous flows

A comparative study of the bilinear, biquadratic quadrilateral element and quadratic triangular element for solving incompressible viscous flows is presented. These elements make use of the Galerkin/Least squares (GLS) stabilized finite element formulation, in which the pressures and velocities are interpolated with equal orders. The Newton-Raphson algorithm is employed in solving the nonlinear FEM equations. All formulae needed for calculating the tangential matrices are derived in details in a form to be easily programmed. Using the method proposed, the numerical solutions of lid-driven cavity flow for Reynolds number of 1000, 5000, 10000 and 20000 are obtained, and the accuracy and converging rate of results from the different elements are compared. The numerical example shows that the quadratic triangular element exhibits the best comprise between the accuracy and convergence rate compared to the other two elements.