Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Least squares methods for $ 2m$th order elliptic boundary-value problems

Authors: J. H. Bramble and A. H. Schatz
Journal: Math. Comp. 25 (1971), 1-32
MSC: Primary 65N99
MathSciNet review: 0295591
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider a general class of boundary-value problems for 2mth order elliptic equations including nonhomogeneous essential boundary conditions and nonselfadjoint problems. Approximation methods involving least squares approximation of the data are presented and corresponding error estimates are proved. These methods can be considered in the category of Rayleigh-Ritz-Galerkin methods and have the special feature that the trial functions need not satisfy the boundary conditions. A special case of the trial functions which is studied are spline functions defined on a uniform mesh of width h (or more generally piecewise polynomial functions). For a given "well set" boundary-value problem for a 2mth order operator the theory presented will provide a method with any prescribed order of accuracy r which is optimal in the sense that the best approximation in the underlying subspace is of order of accuracy r.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N99

Retrieve articles in all journals with MSC: 65N99

Additional Information

Keywords: Rayleigh-Ritz-Galerkin methods, least squares approximation, 2mth order elliptic boundary-value problems, numerical solution of higher order elliptic problems
Article copyright: © Copyright 1971 American Mathematical Society