A spectral element least-squares formulation for incompressible Navier–Stokes flows using triangular nodal elements

We present a least-squares formulation for the numerical solution of incompressible flows using high-order triangular nodal elements. The Fekete points of the triangle are used as nodes and numerical integration is performed using tensor-product Gauss–Legendre rules in a collapsed coordinate system for the standard triangle. A first-order system least-squares (FOSLS) approach based on velocity, pressure, and vorticity is used to allow the use of practical C0 element expansions in each triangle. The numerical results demonstrate spectral convergence for smooth solutions, excellent conservation of mass for steady and unsteady problems of the inflow/outflow type, and the flexibility of using triangles to partition domains where the use of quadrangles would be cumbersome or inefficient.