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Error analysis for Laplace transform —Finite element solution of hyperbolic equations

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Summary

The finite element method with Laplace transform of time variable is proposed for the solution of hyperbolic equations. Error estimates in Hardy spaces of functions with values in Sobolev spaces are derived. Due to the isometric isomorphism of Hardy spaces with weighted Hilbert spaces these estimates are valid also for original formulations of hyperbolic equations.

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References

  1. Agmon, S.: Elliptic Boundary Value Problems. New York, Toronto, London, Melbourne: Van Nostrand, 1965

    Google Scholar 

  2. Babuska, I., Aziz, A.K.: Survey lectures on the mathematical foundation of the finite element method. In: The Mathematical Foundation of Finite Element Method with Applications to Partial Differential Equations. Aziz, A.K. (ed.). New York, San Francisco, London: Academic Press, 1972

    Google Scholar 

  3. Besov, O.V., Iljin, V.P., Nikolskij, S.M.: Integral Representation of Functions and Embedding Theorems (in Russian). Moskva: Science Publ. House, 1975

    Google Scholar 

  4. Brilla, J.: Finite element method in linear viscoelasticity. ZAMM, Sonderheft,54, T47–48 (1974)

    Google Scholar 

  5. Brilla, J.: Generalized variational methods in linear viscoelasticity. In: Hult, J. (ed.). Mechanics of Viscoelastic Media and Bodies. Berlin, Heidelberg, New York: Springer, pp. 215–228 1975

    Google Scholar 

  6. Brilla, J.: Finite element method for quasiparabolic equations. Proc. of IV. Conference on Basic Problems of Numerical Mathematics, MFF UK Prague, pp. 25–36, 1979

  7. Donaldson, T.: A Laplace Transform Calculus for Partial Differential Operators. Memoirs of AMS, n. 143, Providence, 1974

  8. Nečas, J.: Les méthodes directes en theorie des équations elliptiques. Prague: Academia, 1967

    Google Scholar 

  9. Oden, J.T., Reddy, J.N.: An Introduction to the Mathematical Theory of Finite Elements. New York, London, Sydney, Toronto: John Willey and Sons, 1976

    Google Scholar 

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  1. Institute of Applied Mathematics and Computing Technique, Comenius University, CZ-84215, Bratislava, Czechoslovakia

    Jozef Brilla

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  1. Jozef Brilla
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Brilla, J. Error analysis for Laplace transform —Finite element solution of hyperbolic equations. Numer. Math. 41, 55–62 (1983). https://doi.org/10.1007/BF01396305

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  • DOI: https://doi.org/10.1007/BF01396305

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