Adjoint pseudospectral least-squares methods for an elliptic boundary value problem

Authors:
Sang Dong Kim;Byeong-Chun Shin
Affiliations:
Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea;Department of Mathematics, Chonnam National University, Gwangju 500-757, Korea
Venue:
Applied Numerical Mathematics
Year:
2009

Citing 6
Cited 0

First-order system least squares for second-order partial differential equations: part I

SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
First-Order System Least Squares for Second-Order Partial Differential Equations: Part II

SIAM Journal on Numerical Analysis
Finite Element Methods of Least-Squares Type

SIAM Review
First-Order System $\CL\CL^*$ (FOSLL*): Scalar Elliptic Partial Differential Equations

SIAM Journal on Numerical Analysis
Pseudospectral Least-Squares Method for the Second-Order Elliptic Boundary Value Problem

SIAM Journal on Numerical Analysis
First-Order System LL* (FOSLL*) for General Scalar Elliptic Problems in the Plane

SIAM Journal on Numerical Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

The adjoint approach for Legendre pseudospectral least-squares methods is presented by adopting the adjoint first-order systems developed in [Z. Cai, T. Manteuffel, S. McCormick, J. Ruge, First-order system LL^* (FOSLL*): scalar elliptic partial differential equations, SIAM J. Numer. Anal. 39 (2001) 1418-1445]. The discrete adjoint least-squares functional on a polynomial space using Legendre-Gauss-Lobatto points and weights is shown to be equivalent to H^1 norm. The spectral convergence is also provided with several numerical results.