Interpolation approximations based on Gauss-Lobatto-Legendre-Birkhoff quadrature

Authors:
Li-Lian Wang;Ben-yu Guo
Affiliations:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637616, Singapore;Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai E-institute for Computational Science, Chi ...
Venue:
Journal of Approximation Theory
Year:
2009

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Abstract

We derive in this paper the asymptotic estimates of the nodes and weights of the Gauss-Lobatto-Legendre-Birkhoff (GLLB) quadrature formula, and obtain optimal error estimates for the associated GLLB interpolation in Jacobi weighted Sobolev spaces. We also present a user-oriented implementation of the pseudospectral methods based on the GLLB quadrature nodes for Neumann problems. This approach allows an exact imposition of Neumann boundary conditions, and is as efficient as the pseudospectral methods based on Gauss-Lobatto quadrature for PDEs with Dirichlet boundary conditions.