Simplified proofs of error estimates for the least squares method for Dirichlet’s problem

Baker, Garth A.

doi:10.1090/S0025-5718-1973-0327056-0

Simplified proofs of error estimates for the least squares method for Dirichlet’s problem
HTML articles powered by AMS MathViewer

by Garth A. Baker PDF

Math. Comp. 27 (1973), 229-235 Request permission

Abstract:

Recently, Bramble and Schatz have proposed a projection method for approximating the solution of Dirichlet’s problem. Error estimates are derived by the authors using arguments based on certain interpolation theorems for linear operators on Hilbert spaces. It is shown here that simpler and shorter methods can be used to obtain these error estimates.

References

James H. Bramble and Alfred H. Schatz, Rayleigh-Ritz-Galerkin methods for Dirichlet’s problem using subspaces without boundary conditions, Comm. Pure Appl. Math. 23 (1970), 653–675. MR 267788, DOI 10.1002/cpa.3160230408

Higher Order Polygonal Domain Galerkin Approximations in Dirichlet’s Problem

J. H. Bramble and S. R. Hilbert, Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation, SIAM J. Numer. Anal. 7 (1970), 112–124. MR 263214, DOI 10.1137/0707006
James H. Bramble and Vidar Thomée, Semidiscrete least-squares methods for a parabolic boundary value problem, Math. Comp. 26 (1972), 633–648. MR 349038, DOI 10.1090/S0025-5718-1972-0349038-4
J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968 (French). MR 0247243
Martin Schechter, On $L^{p}$ estimates and regularity. II, Math. Scand. 13 (1963), 47–69. MR 188616, DOI 10.7146/math.scand.a-10688