This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
D. Archer, Thesis, Rice University, 1973.
J.H. Bramble and J.E. Osborn, Rate of convergence estimates for nonselfadjoint eigenvalue approximations, Math. Comp. 27(1973), 525–549.
—, —, Approximation of Steklov eigenvalues of nonselfadjoint second order elliptic operators, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A.K. Aziz (ed.), Academic Press, New York, 1972.
E.W. Cheney, Introduction to Approximation Theory, McGraw-Hill, New York, 1966.
P.J. Davis, Interpolation and Approximation, Blaisdell Publishing Co., New York, 1963.
C. DeBoor and B. Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal. 10(1973), 582–606.
J. Douglas, Jr., A superconvergence result for the approximation solution of the heat equation by a colloation method, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A.K. Aziz (ed.), Academic Press, New York, 1972.
J. Douglas, Jr., and T. Dupont, A finite element collocation method for the heat equation, Symposia Mathematica 10, Monograf, Bologna, 1972.
—, —, A finite element collocation method for quasilinear parabolic equations, Math. Comp. 27, (1973), 17–28.
—, —, 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.
—, —, Galerkin approximations for the two point boundary problem using continuous, piecewise polynomial spaces, to appear in Numer. Math.
—, —, Superconvergence for Galerkin methods for the two point boundary problem via local projections, to appear in Numer. Math.
—, —, and M.F. Wheeler, Some superconvergence results for an H1-Galerkin procedure for the heat equation, MRC Report No. 1382 and to appear in the Proceedings of an International Symposium on Computing Methods in Applied Sciences and Engineering, IRIA, Rocquencourt, 1973.
J. Douglas, Jr., T. Dupont, and M.F. Wheeler, A quasi-projection approximation method applied to Galerkin procedures for parabolic and hyperbolic equations, to appear.
—, —, —, A Galerkin procedure for approximating the flux on the boundary for elliptic and parabolic boundary value problems MRC Report No. 1381 and the appear.
T. Dupont, Some L2 error estimates for parabolic Galerkin methods, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A.K. Aziz (ed.), Academic Press, New York, 1972.
B.L. Hulme, One-step piecewise polynomial Galerkin methods for initial value problems, Math. Comp. 26 (1972), 415–426.
J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, vol. 1, Dunod, Paris, 1968.
T.R. Lucas and G.W. Reddien, Some collocation methods for nonlinear boundary value problems, SIAM J. Numer. Anal. 9(1972). 341–356.
V. Thomée, Spline approximation and difference schemes for the heat equation, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A.K. Aziz (ed.), Academic Press, New York, 1972.
V. Thomée, and B. Wendroff, Convergence estimates for Galerkin methods for variable coefficient initial-value problems, to appear.
E.T. Whittaker and G.N. Watson, A Course in Modern Analysis, Cambridge University Press, New York, 1948.
Rights and permissions
Copyright information
© 1974 Springer-Verlag
About this chapter
Cite this chapter
Douglas, J., Dupont, T. (1974). A smoothed collocation method and applications to eigensystem approximation. In: Collocation Methods for Parabolic Equations in a Single Space Variable. Lecture Notes in Mathematics, vol 385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057341
Download citation
DOI: https://doi.org/10.1007/BFb0057341
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06747-4
Online ISBN: 978-3-540-38337-6
eBook Packages: Springer Book Archive