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Galerkin approximations for the two point boundary problem using continuous, piecewise polynomial spaces. (English) Zbl 0331.65051

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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[1] Agmon, S.: Lectures on elliptic boundary value problems. Princeton: Van Nostrand 1965 · Zbl 0142.37401
[2] Ciarlet, P. G., Raviart, P.-A.: The combined effect of curved boundaries and numerical integration in isoparametric finite element methods. The Mathematical foundations of the finite element method. Academic Press 1972 · Zbl 0262.65070
[3] Douglas, J., Jr., Dupont, T.: Some superconvergence results for Galerkin methods for the approximate solution of two point boundary problems. To appear in the Proceedings of a conference on numerical analysis held by the Royal Irish Academy, Dublin, 1972
[4] Herbold, R. J., Varga, R. S.: The effect of quadrature errors in the numerical solution of two-dimensional boundary value problems by variational techniques. Aequationes Math.7, 36-58 (1972) · Zbl 0233.65056
[5] Schatz, A. H.: Private communication
[6] Wheeler, M. F.: An optimalL ? error estimate for Galerkin approximations to solutions of two point boundary problems. SIAM J. Num. Anal.10, 914-917 (1973) · Zbl 0266.65061
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