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
A new method of stabilization for singular perturbation problems with spectral methods
SIAM Journal on Numerical Analysis
A stabilized multidomain approach for singular perturbation problems
Journal of Scientific Computing
Spectral viscosity for convection dominated flow
Journal of Scientific Computing
Analysis of a Discontinuous Least Squares Spectral Element Method
Journal of Scientific Computing
Least-Squares Spectral Collocation for the Navier–Stokes Equations
Journal of Scientific Computing
Journal of Computational Physics
Spectral collocation and radial basis function methods for one-dimensional interface problems
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
| Hi-index | 7.30 |
A least-squares spectral collocation scheme for discontinuous problems is proposed. For the first derivative operator the domain is decomposed in subintervals where the jumps are imposed at the discontinuities. Equal order polynomials are used on all subdomains. For the discretization spectral collocation with Chebyshev polynomials is employed. Fast Fourier transforms are now available. The collocation conditions and the interface conditions lead to an overdetermined system which can be efficiently solved by least-squares. The solution technique will only involve symmetric positive definite linear systems. This approach is further extended to singular perturbation problems where least-squares are used for stabilization. By a suitable decomposition of the domain the boundary layer is well resolved. Numerical simulations confirm the high accuracy of our spectral least-squares scheme.