Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The finite element method in the family of improperly posed problems


Author: Hou De Han
Journal: Math. Comp. 38 (1982), 55-65
MSC: Primary 65M60; Secondary 35R25, 65M30
MathSciNet review: 637286
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The numerical solution of the Cauchy problem for elliptic equations is considered. We reformulate the original problem as a variational inequality problem, which we solve using the finite element method. Moreover, we prove the convergence of the approximate solution.


References [Enhancements On Off] (What's this?)

  • [1] J. Hadamard, Lectures on the Cauchy Problem in Linear Partial Differential Equations, Yale Univ. Press, New Haven, 1923.
  • [2] M. M. Lavrent′ev, On the Cauchy problem for Laplace equation, Izv. Akad. Nauk SSSR. Ser. Mat. 20 (1956), 819–842 (Russian). MR 0087874 (19,426d)
  • [3] L. E. Payne, Bounds in the Cauchy problem for the Laplace equation, Arch. Rational Mech. Anal. 5 (1960), 35–45 (1960). MR 0110875 (22 #1743)
  • [4] L. E. Payne, On a priori bounds in the Cauchy problem for elliptic equations, SIAM J. Math. Anal. 1 (1970), 82–89. MR 0262654 (41 #7259)
  • [5] L. E. Payne, Improperly posed problems in partial differential equations, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1975. Regional Conference Series in Applied Mathematics, No. 22. MR 0463736 (57 #3678)
  • [6] Ivar Ekeland and Roger Temam, Convex analysis and variational problems, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1976. Translated from the French; Studies in Mathematics and its Applications, Vol. 1. MR 0463994 (57 #3931b)
  • [7] Hou De Han and Long An Ying, An iterative method with infinite elements, Math. Numer. Sinica 1 (1979), no. 1, 91–99 (Chinese, with English summary). MR 656882 (83d:65285)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M60, 35R25, 65M30

Retrieve articles in all journals with MSC: 65M60, 35R25, 65M30


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1982-0637286-1
PII: S 0025-5718(1982)0637286-1
Article copyright: © Copyright 1982 American Mathematical Society