A variational formulation for the Chebyshev pseudospectral approximation of Neumann problems
SIAM Journal on Numerical Analysis
Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers
Journal of Computational Physics
Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
Journal of Approximation Theory
Second order Jacobi approximation with applications to fourth-order differential equations
Applied Numerical Mathematics
Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials
Journal of Scientific Computing
Applied Numerical Mathematics
The Laguerre spectral method for solving Neumann boundary value problems
Journal of Computational and Applied Mathematics
Jacobi spectral method with essential imposition of Neumann boundary condition
Applied Numerical Mathematics
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In this paper, we present error estimates of Legendre spectral method with essential imposition of Neumann boundary condition. The algorithm was firstly proposed by Auteri, Parolini and Quartapelle. This method differs from the classical spectral methods for Neumann boundary value problems. The homogeneous boundary condition is satisfied exactly. Moreover, a double diagonalization process is employed, instead of the full stiffness matrices encountered in the classical variational formulation of the problem with a weak natural imposition of the derivative boundary condition. We also consider nonhomogeneous Neumann data by means of a lifting. In particular, the lifting in this paper is expressed explicitly and is different from that by Auteri, Parolini and Quartapelle. For analyzing the numerical errors, some basic results on Legendre quasi-orthogonal approximations are established. The convergence of proposed schemes is proved.