A discrete least squares method

Author:
Peter H. Sammon

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

MSC:
Primary 65L10

MathSciNet review:
0431699

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 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****[2]**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****[3]**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**, 10.1090/S0025-5718-1975-0388788-3

Retrieve articles in *Mathematics of Computation*
with MSC:
65L10

Retrieve articles in all journals with MSC: 65L10

Additional Information

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

Article copyright:
© Copyright 1977
American Mathematical Society