A discrete least squares method
Peter H. Sammon
Math. Comp. 31 (1977), 60-65
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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.
G. Ciarlet and P.-A.
Raviart, General Lagrange and Hermite interpolation in
𝑅ⁿ with applications to finite element methods, Arch.
Rational Mech. Anal. 46 (1972), 177–199. MR 0336957
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
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
(52 #9622), http://dx.doi.org/10.1090/S0025-5718-1975-0388788-3
- P. G. CIARLET & P.-A. RAVIART, "General Lagrange and Hermite interpolation in with applications to finite element methods," Arch. Rational Mech. Anal., v. 46, 1972, pp. 177-199. MR 49 #1730. MR 0336957 (49:1730)
- P. G. CIARLET & P.-A RAVIART, "The combined effects of curved boundaries and numerical integration in isoparametric methods," The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, Editor), Academic Press, New York and London, 1972, pp. 409-474. MR 0421108 (54:9113)
- R. D. RUSSELL & J. M. VARAH, "A comparison of global methods for linear two-point boundary value problems," Math. Comp., v. 29, 1975, pp. 1007-1019. MR 0388788 (52:9622)
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