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Multidimensional characteristic Galerkin methods for hyperbolic systems
Author(s) -
Ostkamp S.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19970910)20:13<1111::aid-mma903>3.0.co;2-1
Subject(s) - mathematics , galerkin method , discontinuous galerkin method , mathematical analysis , calculus (dental) , finite element method , physics , thermodynamics , medicine , dentistry
We consider characteristic Galerkin methods for the solution of hyperbolic systems of partial differential equations of first order. A new recipe for the construction of approximate evolution operators is given in order to derive consistent methods. With the help of semigroup theory we derive error estimates for classes of characteristic Galerkin methods. The theory is applied to the wave equation and also to the Euler equations of gas dynamics. In the latter case one can show that Fey's genuinely multidimensional method can be reinterpreted as a characteristic Galerkin method. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.