Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Error bounds for Galerkin’s method for monotone operator equations
HTML articles powered by AMS MathViewer

by Martin H. Schultz
Proc. Amer. Math. Soc. 35 (1972), 227-229
DOI: https://doi.org/10.1090/S0002-9939-1972-0297123-X

Abstract:

An abstract theorem, generalizing a result of Nitsche, is proved. This gives sharp error bounds for the Galerkin method for approximating the solutions of a large class of non-linear operator equations in Hilbert spaces.
References
  • Felix E. Browder, Approximation-solvability of nonlinear functional equations in normed linear spaces, Arch. Rational Mech. Anal. 26 (1967), 33–42. MR 220119, DOI 10.1007/BF00283857
  • P. G. Ciarlet, M. H. Schultz, and R. S. Varga, Numerical methods of high-order accuracy for nonlinear boundary value problems. V. Monotone operator theory, Numer. Math. 13 (1969), 51–77. MR 250496, DOI 10.1007/BF02165273
  • J. Nitsche, Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens, Numer. Math. 11 (1968), 346–348 (German). MR 233502, DOI 10.1007/BF02166687
  • J. Nitsche, Verfahren von Ritz und Spline-Interpolation bei Sturm-Liouville-Randwertproblemen, Numer. Math. 13 (1969), 260–265 (German). MR 278532, DOI 10.1007/BF02167557
  • J. Nitsche, Konvergenz des Ritz-Galerkinschen Verfahrens bei nichtlinearen Operatorgleichungen, Iterationsverfahren, Numerische Mathematik, Approximationstheorie, Internat. Schriftenreihe Numer. Math., Vol. 15, Birkhäuser, Basel, 1970, pp. 75–81 (German). (Tagung Nichtlineare Aufgaben Numer. Math., Oberwolfach, 1968),. MR 0378406
  • Martin H. Schultz, $L^{2}$ error bounds for the Rayleigh-Ritz-Galerkin method, SIAM J. Numer. Anal. 8 (1971), 737–748. MR 298918, DOI 10.1137/0708067
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 65J05
  • Retrieve articles in all journals with MSC: 65J05
Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 227-229
  • MSC: Primary 65J05
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0297123-X
  • MathSciNet review: 0297123