A discrete least squares method
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- by Peter H. Sammon PDF
- Math. Comp. 31 (1977), 60-65 Request permission
Abstract:
We consider a discrete least squares approximation to the solution of a two-point boundary value problem for a 2mth order elliptic operator. We describe the approximation space of piecewise polynomials and devise a Gaussian quadrature rule that is suitable for replacing the integrals in the usual least squares method. We then show that if the quadrature rule is of sufficient accuracy, the optimal order of convergence is obtained.References
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- P. G. Ciarlet and P.-A. Raviart, The combined effect of curved boundaries and numerical integration in isoparametric finite element methods, The mathematical foundations of the finite element method with applications to partial differential equations (Proc. Sympos., Univ. Maryland, Baltimore, Md., 1972) Academic Press, New York, 1972, pp. 409–474. MR 0421108
- R. D. Russell and J. M. Varah, A comparison of global methods for linear two-point boundary value problems, Math. Comput. 29 (1975), no. 132, 1007–1019. MR 0388788, DOI 10.1090/S0025-5718-1975-0388788-3
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Math. Comp. 31 (1977), 60-65
- MSC: Primary 65L10
- DOI: https://doi.org/10.1090/S0025-5718-1977-0431699-7
- MathSciNet review: 0431699