Fairweather, Graeme; Keast, Patrick; Diaz, Julio Cesar On the \(H^{-1}\)-Galerkin method for second-order linear two-point boundary value problems. (English) Zbl 0546.65056 SIAM J. Numer. Anal. 21, 314-326 (1984). The authors consider \(H^{-1}\)-Galerkin methods for two-point boundary value problems. These \(H^{-1}\) methods were introduced by H. H. Rachford jun. and M. F. Wheeler [Math. Aspects finite Elem. partial Differ. Equat., Proc. Symp. Madison 1974, 353-382 (1974; Zbl 0347.65037)] for the case of Dirichlet boundary conditions. In the present paper the \(H^{-1}\)-methods are formulated subject to further types of boundary conditions, and the corresponding error analysis is performed. The authors refer to a new subroutine package named ROWCOL for the solution of the corresponding linear algebraic systems. The results are illustrated by means of some numerical examples. Reviewer: E.Wagenführer Cited in 1 ReviewCited in 1 Document MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations 35K20 Initial-boundary value problems for second-order parabolic equations Keywords:Galerkin methods; error analysis; subroutine package; ROWCOL; numerical examples Citations:Zbl 0347.65037 PDFBibTeX XMLCite \textit{G. Fairweather} et al., SIAM J. Numer. Anal. 21, 314--326 (1984; Zbl 0546.65056) Full Text: DOI