Least-square finite elements for Stokes problem
Computer Methods in Applied Mechanics and Engineering
Least-squares finite element method for fluid dynamics
Computer Methods in Applied Mechanics and Engineering
Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation
SIAM Journal on Numerical Analysis
Least-squares spectral elements applied to the Stokes problem
Journal of Computational Physics
A Least-Squares Spectral Element Formulation for the Stokes Problem
Journal of Scientific Computing
Least-squares spectral collocation for discontinuous and singular perturbation problems
Journal of Computational and Applied Mathematics
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
Journal of Computational Physics
Spectral collocation schemes on the unit disc
Journal of Computational Physics
Mass- and Momentum Conservation of the Least-Squares Spectral Element Method for the Stokes Problem
Journal of Scientific Computing
Direct Minimization of the least-squares spectral element functional - Part I: Direct solver
Journal of Computational Physics
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
hp-Adaptive least squares spectral element method for hyperbolic partial differential equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Hi-index | 7.29 |
From the literature, it is known that the Least-Squares Spectral Element Method (LSSEM) for the stationary Stokes equations performs poorly with respect to mass conservation but compensates this lack by a superior conservation of momentum. Furthermore, it is known that the Least-Squares Spectral Collocation Method (LSSCM) leads to superior conservation of mass and momentum for the stationary Stokes equations. In the present paper, we consider mass and momentum conservation of the LSSCM for time-dependent Stokes and Navier-Stokes equations. We observe that the LSSCM leads to improved conservation of mass (and momentum) for these problems. Furthermore, the LSSCM leads to the well-known time-dependent profiles for the velocity and the pressure profiles. To obtain these results, we use only a few elements, each with high polynomial degree, avoid normal equations for solving the overdetermined linear systems of equations and introduce the Clenshaw-Curtis quadrature rule for imposing the average pressure to be zero. Furthermore, we combined the transformation of Gordon and Hall (transfinite mapping) with the least-squares spectral collocation scheme to discretize the internal flow problems.