Adjoint pseudospectral least-squares methods for an elliptic boundary value problem
Applied Numerical Mathematics
Spectral collocation and radial basis function methods for one-dimensional interface problems
Applied Numerical Mathematics
The least-squares pseudo-spectral method for Navier-Stokes equations
Computers & Mathematics with Applications
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The least-squares Legendre and Chebyshev pseudospectral methods are presented for a first-order system equivalent to a second-order elliptic partial differential equation. Continuous and discrete homogeneous least-squares functionals using Legendre and Chebyshev weights are shown to be equivalent to the H1(\Omega)$ norm and Chebyshev-weighted Div-Curl norm over appropriate polynomial spaces, respectively. The spectral error estimates are derived. The block diagonal finite element preconditioner is developed for the both cases. Several numerical tests are demonstrated on the spectral discretization errors and on performances of the finite element preconditioner.