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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 1-32, 2025/01/15
We study the numerical approximation of a coupled hyperbolic-parabolic system by a family of discontinuous Galerkin (DG) space-time finite element methods. The model is rewritten as a first-order evolutionary problem that is treated by a unified abstract solution theory. For the discretization in space, generalizations of the distribution gradient and divergence operators on broken polynomial spaces are defined. Since their skew-selfadjointness is perturbed by boundary surface integrals, adjustments are introduced such that the skew-selfadjointness of the discrete counterpart of the total system's first-order differential operator in space is recovered. Well-posedness of the fully discrete problem and error estimates for the DG approximation in space and time are proved.
Keywords: Coupled hyperbolic-parabolic problem, first-order system, Picard's theorem, discontinuous Galerkin space-time discretization, error estimates