Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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.

 

The finite element method with penalty
HTML articles powered by AMS MathViewer

by Ivo Babuška PDF
Math. Comp. 27 (1973), 221-228 Request permission

Abstract:

An application of the penalty method to the finite element method is analyzed. For a model Poisson equation with homogeneous Dirichlet boundary conditions, a variational principle with penalty is discussed. This principle leads to the solution of the Poisson equation by using functions that do not satisfy the boundary condition. The rate of convergence is discussed.
References
  • J. H. Bramble and A. H. Schatz, On the numerical solution of elliptic boundary value problems by least squares approximation of the data, Numerical Solution of Partial Differential Equations, II (SYNSPADE 1970) (Proc. Sympos., Univ. of Maryland, College Park, Md., 1970) Academic Press, New York, 1971, pp. 107–131. MR 0273837
  • Jean Pierre Aubin and Hermann G. Burchard, Some aspects of the method of the hypercircle applied to elliptic variational problems, Numerical Solution of Partial Differential Equations, II (SYNSPADE 1970) (Proc. Sympos., Univ. of Maryland, College Park, Md., 1970) Academic Press, New York, 1971, pp. 1–67. MR 0285136
  • Jean-Pierre Aubin, Approximation of elliptic boundary-value problems, Pure and Applied Mathematics, Vol. XXVI, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London-Sydney, 1972. MR 0478662
    • I. Babuška, "The finite element method for elliptic differentiation equations," Numerical Solution of Partial Differential Equations, II (SYNSPADE 1970) (Proc. Sympos., Univ. of Maryland, College Park, Md., 1970), Academic Press, New York, 1971, pp. 69-106. MR 42 #8712. I. Babuška, Numerical Solution of Boundary Value Problems by the Perturbed Variational Principle, Institute for Fluid Dynamics and Appl. Math., Technical Note BN-624, University of Maryland, College Park, Md., 1969.
  • Ivo Babuška, The finite element method for elliptic equations with discontinuous coefficients, Computing (Arch. Elektron. Rechnen) 5 (1970), 207–213. MR 277119, DOI 10.1007/bf02248021
  • J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abh. Math. Sem. Univ. Hamburg 36 (1971), 9–15 (German). MR 341903, DOI 10.1007/BF02995904
  • J.-L. Lions, Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles, Dunod, Paris; Gauthier-Villars, Paris, 1968 (French). Avant propos de P. Lelong. MR 0244606
  • Approximation by hill functions, Comment. Math. Univ. Carolinae 11 (1970), 787–811. MR 292309
  • Ivo Babuška, The rate of convergence for the finite element method, SIAM J. Numer. Anal. 8 (1971), 304–315. MR 287715, DOI 10.1137/0708031
  • Ivo Babuška, Approximation by hill functions. II, Comment. Math. Univ. Carolinae 13 (1972), 1–22. MR 305550
  • Ivo Babuška, Error-bounds for finite element method, Numer. Math. 16 (1970/71), 322–333. MR 288971, DOI 10.1007/BF02165003
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65N30
  • Retrieve articles in all journals with MSC: 65N30
Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Math. Comp. 27 (1973), 221-228
  • MSC: Primary 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-1973-0351118-5
  • MathSciNet review: 0351118