Adaptive Finite Element Methods for the Compressible Euler Equations

Hartmann, Ralf

German Title: Adaptive Finite Elemente Methoden für die kompressiblen Eulergleichungen

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DOI: 10.11588/heidok.00002488
URN: urn:nbn:de:bsz:16-opus-24885
URL: http://www.ub.uni-heidelberg.de/archiv/2488

Translation of abstract (English)

In this thesis we introduce a discontinuous Galerkin method for the numerical solution of hyperbolic conversation laws, as for example the compressible Euler equations of gas dynamics. Based on this finite element method, we develop an adaptive algorithm for the efficient computation of physically relevant quantities of the solution. This includes a posteriori error estimation of the error in the computed quantity as well as adaptive mesh design specifically tailored to the efficient computation of this quantity. We illustrate this approach by several different hyperbolic problems in combination with various different target quantities, including the efficient computation of drag and lift coefficients of airfoils immersed in inviscid compressible gas flows.

Document type:	Dissertation
Supervisor:	Rannacher, Prof. Rolf
Date of thesis defense:	15 July 2002
Date Deposited:	26 Jul 2002 00:00
Date:	2002
Faculties / Institutes:	The Faculty of Mathematics and Computer Science > Institut für Mathematik
DDC-classification:	510 Mathematics
Uncontrolled Keywords:	kompressible Eulergleichungen , unstetiges Galerkin Verfahren , a posteriori Fehlerschätzung , adaptive Gitterverfeinerung , Zielgrössencompressible Euler equations , discontinuous Galerkin method , a posteriori error estimation , adaptive mesh refinement , target quantities