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.

**[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 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, " 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)**

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