SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
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
Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials
Journal of Scientific Computing
Applied Numerical Mathematics
Error analysis of Legendre spectral method with essential imposition of Neumann boundary condition
Applied Numerical Mathematics
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In this paper, we propose Jacobi spectral method with essential imposition of Neumann boundary condition. This method differs from the classical spectral methods for Neumann boundary value problems. The homogeneous boundary condition is satisfied exactly. Moreover, a diagonal or tridiagonal matrix 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. For analyzing the numerical error, some basic results on Jacobi quasi-orthogonal and orthogonal approximations are established. The convergence of proposed schemes is proved. Numerical results demonstrate the efficiency of this approach and coincide well with theoretical analysis.