TY - GEN A1 - Walter, Artur T1 - Ein Finite-Element-Verfahren zur numerischen Lösung von Erhaltungsgleichungen. N2 - 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. T3 - ZIB-Report - TR-89-03 Y1 - 1989 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/459 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-4597 ER -