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Ein Finite-Element-Verfahren zur numerischen Lösung von Erhaltungsgleichungen.

Please always quote using this URN: urn:nbn:de:0297-zib-4597
  • A new approach for the discretisation of hyperbolic conservation laws via a finite element method is developed and analysed. Appropriate forms of the Eulers equation of gas dynamic are considered to employ the algorithm in a reasonable way for this system of nonlinear equations. Both mathematical and physical stability results are obtained. A main part of the paper is devoted to the convergence proof with energy methods under strong regularity of the solution of a scalar nonlinear conservation law. Some hints on the implementation and numerical results for the calculation of transonic gasflow through a Laval nozzle are given. The necessary amount of numerical work is compared to an established finite difference method and the efficiency of the algorithm is shown. A survey on recent literature about finite element methods for hyperbolic problem is included.

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Author:Artur Walter
Document Type:ZIB-Report
Date of first Publication:1989/02/16
Series (Serial Number):ZIB-Report (TR-89-03)
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