Simplified proofs of error estimates for the least squares method for Dirichlet’s problem
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- 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 J. H. Bramble, T. Dupont & V. Thomée, Higher Order Polygonal Domain Galerkin Approximations in Dirichlet’s Problem, MRC Technical Summary Report #1213, March 1972.
- 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 V. Thomée, Private communication.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Math. Comp. 27 (1973), 229-235
- MSC: Primary 65N15
- DOI: https://doi.org/10.1090/S0025-5718-1973-0327056-0
- MathSciNet review: 0327056