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On the Finite Element Approximation for Parabolic Equations: An Operator Theoretical Approach

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Computing Methods in Applied Sciences and Engineering

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 134))

Abstract

The purpose of the present paper is to make an operator theoretical study of the finite element method applied to the initial boundary value problems for parabolic equations. As a consequence we shall derive estimates of the rate of convergence which are valid in t > 0 even when no smoothness assumption on the initial data is made. Actually, various works by many authors have been done so far concerning the application of the finite element method to parabolic equations: e.g., Zlámal [21], Bramble-Thomée [4], Douglas -Dupont [6], Babuska-Azis [1] and Ushijima [17].

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Tokyo, Hongo, Tokyo 113, Japan

    Hiroshi Fujita

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  1. Hiroshi Fujita
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Editor information

Editors and Affiliations

  1. Domaine de Voluceau BP 105, IRIA LABORIA, 78150, Rocquencourt, Le Chesnay, France

    R. Glowinski  & J. L. Lions  & 

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© 1976 Springer-Verlag Berlin Heidelberg

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Fujita, H. (1976). On the Finite Element Approximation for Parabolic Equations: An Operator Theoretical Approach. In: Glowinski, R., Lions, J.L. (eds) Computing Methods in Applied Sciences and Engineering. Lecture Notes in Economics and Mathematical Systems, vol 134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85972-4_10

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  • DOI: https://doi.org/10.1007/978-3-642-85972-4_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07990-3

  • Online ISBN: 978-3-642-85972-4

  • eBook Packages: Springer Book Archive

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