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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Error bounds for Galerkin’s method for monotone operator equations
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by Martin H. Schultz PDF
Proc. Amer. Math. Soc. 35 (1972), 227-229 Request permission

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 (Tagung Nichtlineare Aufgaben Numer. Math., Oberwolfach, 1968) Internat. Schriftenreihe Numer. Math., Vol. 15, Birkhäuser, Basel, 1970, pp. 75–81 (German). 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
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Additional 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