A discrete least squares method

Author:
Peter H. Sammon

Journal:
Math. Comp. **31** (1977), 60-65

MSC:
Primary 65L10

DOI:
https://doi.org/10.1090/S0025-5718-1977-0431699-7

MathSciNet review:
0431699

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Abstract: We consider a discrete least squares approximation to the solution of a two-point boundary value problem for a 2*m*th 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.

**[1]**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)****[2]**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)****[3]**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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DOI:
https://doi.org/10.1090/S0025-5718-1977-0431699-7

Article copyright:
© Copyright 1977
American Mathematical Society