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
Issues Related to Least-Squares Finite Element Methods for the Stokes Equations
SIAM Journal on Scientific Computing
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
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
From the literature it is known that spectral least-squares schemes perform poorly with respect to mass conservation and compensate this lack by a superior conservation of momentum. This should be revised, since the here presented new least-squares spectral collocation scheme leads to an outstanding performance with respect to conservation of momentum and mass. The reasons can be found in using only a few elements, each with high polynomial degree, avoiding normal equations for solving the overdetermined linear systems of equations and by introducing 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 our least-squares spectral collocation scheme to discretize the internal flow problems.