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Superconvergence for Galerkin methods for the two point boundary problem via local projections. (English) Zbl 0281.65046

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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References:
[1] Boor, C., de, Swartz, B.: Collocation at Gaussian points. To appear · Zbl 0232.65065
[2] Bramble, J. H., Schatz, A. H.: Rayleigh-Ritz-Galerkin methods for Dirichlet’s problem using subspaces without boundary conditions. Comm. Pure Appl. Math.23, 653-675 (1970) · Zbl 0204.11102
[3] Ciarlet, P. G., Schultz, M. H., Varga, R. S.: Numerical methods of high-order accuracy for nonlinear boundary value problems, I. Numer. Math.9, 394-430 (1967) · Zbl 0155.20403
[4] Davis, P. J.: Interpolation and approximation. New York: Blaisdell 1963 · Zbl 0111.06003
[5] 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 the Conference on Numerical Analysis, Royal Irish Academy, Dublin, 1972
[6] Douglas, J., Jr., Dupont, T.: A superconvergence result for the approximate solution of the heat equation by a collocation method. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A. K. Aziz (ed.). New York: Academic Press 1972
[7] Douglas, J., Jr., Dupont, T.: The approximate solution of nonlinear parabolic equations by collocation methods usingC 1-piecewise-polynomial spaces, to appear
[8] Nitsche, J.: Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens. Numer. Math.11, 346-348 (1968) · Zbl 0175.45801
[9] Thomée, V.: Spline approximation and difference schemes for the heat equation (same book as in 6 above)
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