Adjoint pseudospectral least-squares methods for an elliptic boundary value problem (Q999081)

The adjoint approach for Legendre pseudospectral least-squares methods is presented by adopting the adjoint first-order systems developed by \textit{Z. Cai, T. Manteuffel, S. McCormick} and \textit{J. Ruge} [SIAM J. Numer. Anal. 39, No.~4, 1418--1445 (2001; Zbl 1008.65085)]. The discrete adjoint least-squares functional on a polynomial space using Legendre-Gauss-Lobatto points and weights is shown to be equivalent to the \(H^{1}\) norm. The spectral convergence is also provided with several numerical results.