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 C-0 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. (c) 2006 Elsevier Inc. All rights reserved.