Advertisement

Smooth and non-smooth data error estimates for the homogeneous equation

  • Vidar Thomée
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1054)

Keywords

Parabolic Equation Galerkin Method Error Equation Homogeneous Equation Positive Semidefinite 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.H. Bramble, A.H. Schatz, V. Thomée, and L.B. Wahlbin, Some convergence estimates for semidiscrete Galerkin type approximations for parabolic equations. SIAM J. Numer. Anal. 14, 218–241(1977).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    J. Blair, Approximate solution of elliptic and parabolic boundary value problems, Thesis, Univ. of California, Berkeley (1970).Google Scholar
  3. 3.
    V. Thomée, Some convergence results for Galerkin methods for parabolic boundary value problems. Mathematical Aspects of Finite Elements in Partial Differential Equations, pp. 55–88. C. de Boor ed., Academic Press, New York(1974).Google Scholar
  4. 4.
    H.-P. Helfrich, Fehlerabschätzungen fűr das Galerkinverfahren zur Lösung von Evolutionsgleichungen. Manuscr. Math. 13, 219–235(1974).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    H. Fujita and A. Mizutani, On the finite element method for parabolic equations. I. J. Math. Soc. Japan 28, 749–771(1976).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    M. Huang and V. Thomée, Some convergence estimates for semidiscrete type schemes for time-dependent nonselfadjoint parabolic equations. Math. Comput. 37, 327–346 (1981).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    M. Luskin and R. Rannacher, On the smoothing property of the Galerkin method for parabolic equations. SIAM J. Numer. Anal. 19, 93–113(1982).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    P.H. Sammon, Convergence estimates for semidiscrete parabolic equation approximations. SIAM J. Numer. Anal. 19, 68–92(1982).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    V. Thomée, Negative norm estimates and superconvergence in Galerkin methods for parabolic problems. Math. Comput. 34, 93–113(1980).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Vidar Thomée

There are no affiliations available

Personalised recommendations