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An Adaptive Discontinuous Finite Element Method for the Transport Equation.

Please always quote using this URN: urn:nbn:de:0297-zib-579
  • In this paper we introduce a discontinuous finite element method. In our approach, it is possible to combine the advantages of finite element and finite difference methods. The main ingredients are numerical flux approximation and local orthogonal basis functions. The scheme is defined on arbitrary triangulations and can be easily extended to nonlinear problems. Two different error indicators are derived. Especially the second one is closely connected to our approach and able to handle arbitrary variing flow directions. Numerical results are given for boundary value problems in two dimensions. They demonstrate the performance of the scheme, combined with the two error indicators. {\bf Key words:} neutron transport equation, discontinuous finite element, adaptive grid refinement. {\bf Subject classifications:} AMS(MOS) 65N30, 65M15.

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Author:Jens Lang, Artur Walter
Document Type:ZIB-Report
Tag:adaptive grid refinement; discontinuous finite element; neutron transport equation
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M15 Error bounds
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:1991/06/11
Series (Serial Number):ZIB-Report (SC-91-07)
Published in:Appeared in: Journal of Computational Physics 117 (1995) 28-34.
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