Mathematics of Computation

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

 

 

Negative norm estimates and superconvergence in Galerkin methods for parabolic problems


Author: Vidar Thomée
Journal: Math. Comp. 34 (1980), 93-113
MSC: Primary 65N15; Secondary 65N30
MathSciNet review: 551292
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Negative norm error estimates for semidiscrete Galerkin-finite element methods for parabolic problems are derived from known such estimates for elliptic problems and applied to prove superconvergence of certain procedures for evaluating point values of the exact solution and its derivatives.


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

  • [1] J. H. BRAMBLE & A. H. SCHATZ, "Higher order local accuracy by averaging in the finite element method," Math.,Comp., v. 31, 1977, pp. 94-111. MR 0431744 (55:4739)
  • [2] J. H. BRAMBLE, A. H. SCHATZ, V. THOMÉE & L. B. WAHLBIN, "Some convergence estimates for semidiscrete Galerkin type approximations for parabolic equations," SIAM J. Numer. Anal., v. 14, 1977, pp. 218-241. MR 0448926 (56:7231)
  • [3] J. DOUGLAS, JR., T. DUPONT & M. F. WHEELER, "A quasi-projection analysis of Galerkin methods for parabolic and hyperbolic equations," Math. Comp., v. 32, 1978, pp. 345-362. MR 0495012 (58:13780)
  • [4] A. LOUIS & F. NATTERER, "Acceleration of convergence for finite element solutions of the Poisson equation on irregular meshes." (Preprint 1977.)
  • [5] V. THOMÉE, "High order local approximations to derivatives in the finite element method," Math. Comp., v. 31, 1977, pp. 652-660. MR 0438664 (55:11572)
  • [6] M. F. WHEELER , "A priori $ {L_2}$ error estimates for Galerkin approximations to parabolic partial differential equations," SIAM J. Numer. Anal., v. 10, 1973, pp. 723-759. MR 0351124 (50:3613)
  • [7] M. F. WHEELER, " $ {L_\infty }$ estimates of optimal order for Galerkin methods for one dimensional second order parabolic and hyperbolic equations," SIAM J. Numer. Anal., v. 10, 1973, pp. 908-913. MR 0343658 (49:8398)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N15, 65N30

Retrieve articles in all journals with MSC: 65N15, 65N30


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1980-0551292-5
Article copyright: © Copyright 1980 American Mathematical Society