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Finite Element Multistep Methods for Parabolic Equations

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Finite Elemente und Differenzenverfahren

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Abstract

The initial-boundary value problem for a linear equation in an infinite cylinder under the Dirichlet boundary condition is solved by applying the finite element discretization in the space dimension and Ao-stable multistep discretizations in time. The scheme is unconditionally stable. There is given an error bound under the assumption that the initial value of the solution belongs to L2 only.

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References

  1. Crouzeix, M.: Thesis. Université Paris VI, to appear.

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  2. Cryer, C.W.: A New Class of Highly Stable Methods: Ao-stable Methods. BIT 13 (1973), 153–159.

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  6. Thomée, V.: Some Convergence Results for Galerkin Methods for Parabolic Boundary Value Problems, to appear.

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  7. Zlámal, M.: Finite Element Multistep Discretizations of Parabolic Problems, to appear in Math.Comp.

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Authors and Affiliations

  1. Technical University, Obránců míru 21, 602 00, Brno, Czechoslovakia

    Miloš Zlámal

Authors
  1. Miloš Zlámal
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Editor information

J. Albrecht L. Collatz

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© 1975 Springer Basel AG

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Zlámal, M. (1975). Finite Element Multistep Methods for Parabolic Equations. In: Albrecht, J., Collatz, L. (eds) Finite Elemente und Differenzenverfahren. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 28. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5861-8_11

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  • DOI: https://doi.org/10.1007/978-3-0348-5861-8_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5862-5

  • Online ISBN: 978-3-0348-5861-8

  • eBook Packages: Springer Book Archive

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