Barbeiro, S.; Ferreira, J. A.; Grigorieff, R. D. Supraconvergence of a finite difference scheme for solutions in \(H^S(0,L)\). (English) Zbl 1087.65070 IMA J. Numer. Anal. 25, No. 4, 797-811 (2005). The paper deals with the numerical analysis of linear two-point boundary value problems. The authors study the convergence properties of a centered finite difference scheme. The main statement is a supraconvergence theorem showing second order convergence for solutions in the Sobolov space \(H^3\). The main idea in the proof is to recognize that the finite difference scheme is equivalent to a fully discrete linear finite element method. Finally, the proposed order of convergence of the numerical scheme applied to a test example is shown. Reviewer: Johannes Schropp (Konstanz) Cited in 22 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 65L12 Finite difference and finite volume methods for ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations Keywords:variational formulation; linear two-point boundary value problems; convergence; centered finite difference scheme; supraconvergence; finite element method; numerical example PDFBibTeX XMLCite \textit{S. Barbeiro} et al., IMA J. Numer. Anal. 25, No. 4, 797--811 (2005; Zbl 1087.65070) Full Text: DOI