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On the finite element approximation for evolution equations of parabolic type

Time Dependant Problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 704)

Keywords

  • Finite Element Method
  • Parabolic Equation
  • Neumann Boundary Condition
  • Adjoint Operator
  • Parabolic Type

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References

  1. Y. Fujie and H. Tanabe, On some parabolic equations of evolution in Hilbert space, Osaka J. Math., 10 (1973), 115–130.

    MathSciNet  MATH  Google Scholar 

  2. H. Fujita, On the finite element approximation for parabolic equations: an operator theoretical approach, Proceedings of the 2nd IRIA symposium on computing methods in applied sciences and engineering, 1975, December, Springer LN in Econ. and Math. Syst. 134, (1976), 171–192.

    MathSciNet  Google Scholar 

  3. H. Fujita, On the semi-discrete finite element approximation for the evolution equation ut+A(t)u=0 of parabolic type, Topics in Numerical Analysis, Vol. 3 (Proceedings of Conference on Numerical Analysis, Dublin, 1976, August), Academic Press, London, to appear, 425–437.

    Google Scholar 

  4. H. Fujita and A. Mizutani, On the finite element method for parabolic equations, I: Approximation of holomorphic semi-groups, J. Math. Soc. Japan, 28 (1976), 749–771.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. H. Fujita and A. Mizutani, Remarks on the finite element method for parabolic equations with higher accuracy, Proceedings of Japan-France seminar on functional analysis and numerical analysis, 1976, September, to appear.

    Google Scholar 

  6. H. P. Helfrich, Fehlerabschätzungen für das Galerkinverfahren zür Lösung von Evolutionsgleichungen, Manus. Math., 13 (1974), 219–235.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. H. P. Helfrich, Lokale Konvergenz des Galerkinverfahrens bei Gleichungen vom parabolischen Typ in Hilberträumen, Thesis, 1975.

    Google Scholar 

  8. T. Kato, Abstract evolution equations of parabolic type in Banach and Hilbert spaces, Nagoya Math. J., 5 (1961), 93–125.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin-Heidelberg-New York, 1966.

    CrossRef  MATH  Google Scholar 

  10. P. A. Raviart, Multistep methods and parabolic equations, Proceedings of Japan-France seminar on functional analysis and numerical analysis, 1976, September, to appear.

    Google Scholar 

  11. P. E. Sobolevskii, Parabolic type equations in Banach spaces, Trudy Moscow Math., 10 (1961), 297–350.

    MathSciNet  Google Scholar 

  12. T. Suzuki, An abstract study of Galerkin's method for the evolution equation ut + A(t)u = 0 of parabolic type with the Neumann boundary condition, to appear in J. Fac. Sci. Univ. Tokyo.

    Google Scholar 

  13. H. Tanabe, On the equation of evolution in a Banach space, Osaka Math. J., 12 (1960), 363–376.

    MathSciNet  MATH  Google Scholar 

  14. M. Zlámal, Curved elements in the finite element method I, SIAM J. Numer. Anal., 10 (1973), 229–240.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1979 Springer-Verlag

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Fujita, H., Suzuki, T. (1979). On the finite element approximation for evolution equations of parabolic type. In: Glowinski, R., Lions, J.L., Laboria, I. (eds) Computing Methods in Applied Sciences and Engineering, 1977, I. Lecture Notes in Mathematics, vol 704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063621

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  • DOI: https://doi.org/10.1007/BFb0063621

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09123-3

  • Online ISBN: 978-3-540-35411-6

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