Spectral methods on triangles and other domains
Journal of Scientific Computing
Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Tensor product Gauss-Lobatto points are Fekete points for the cube
Mathematics of Computation
An Algorithm for Computing Fekete Points in the Triangle
SIAM Journal on Numerical Analysis
Least-squares spectral elements applied to the Stokes problem
Journal of Computational Physics
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Least-Squares Spectral Collocation for the Navier–Stokes Equations
Journal of Scientific Computing
Spectral element methods on triangles and quadrilaterals: comparisons and applications
Journal of Computational Physics
Algebraic multigrid for higher-order finite elements
Journal of Computational Physics
Journal of Computational Physics
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
Hi-index | 31.45 |
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.