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
Agmon, S.: Elliptic Boundary Value Problems. New York, Toronto, London, Melbourne: Van Nostrand, 1965
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
Besov, O.V., Iljin, V.P., Nikolskij, S.M.: Integral Representation of Functions and Embedding Theorems (in Russian). Moskva: Science Publ. House, 1975
Brilla, J.: Finite element method in linear viscoelasticity. ZAMM, Sonderheft,54, T47–48 (1974)
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
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
Donaldson, T.: A Laplace Transform Calculus for Partial Differential Operators. Memoirs of AMS, n. 143, Providence, 1974
Nečas, J.: Les méthodes directes en theorie des équations elliptiques. Prague: Academia, 1967
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
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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