Paper Info
Title
Pseudospectral Least-Squares Method for the Second-Order Elliptic Boundary Value Problem
Abstract
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.
Year
DOI
Venue
2003
10.1137/S0036142901398234
SIAM J. Numerical Analysis
Keywords
Field
DocType
spectral discretization error,least-squares functionals,chebyshev weight,spectral error estimate,least-squares legendre,finite element preconditioner,pseudospectral least-squares method,chebyshev-weighted div-curl norm,chebyshev pseudospectral method,first-order system equivalent,second-order elliptic boundary value,block diagonal finite element,pseudospectral method,elliptic boundary value problem,least square method
Chebyshev pseudospectral method,Mathematical analysis,Chebyshev equation,Legendre polynomials,Pseudospectral optimal control,Gauss pseudospectral method,Finite element method,Elliptic partial differential equation,Mathematics,Elliptic boundary value problem
Journal
Volume
Issue
ISSN
41
4
0036-1429
Citations 
PageRank 
References 
3
0.82
4
Authors
3
Name
Order
Citations
PageRank
Sang Dong Kim1359.22
Hyung-Chun Lee25710.52
Byeong Chun Shin372.56