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Immersed interface methods for elliptic boundary value problemsRutka, Vita. January 2005 (has links) (PDF)
Kaiserslautern, Techn. University, Diss., 2005.
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A-posteriori-Fehlerschätzer für Sattelpunktsformulierungen nicht-homogener RandwertproblemeLipinski, Mario Kai. January 2004 (has links) (PDF)
Bochum, Universiẗat, Diss., 2004.
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Flache Lösungen des Vlasov-Poisson-SystemsDietz, Svetlana. Unknown Date (has links)
Universiẗat, Diss., 2002--München.
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Eine cache-optimale Implementierung der Finite-Elemente-MethodeGünther, Frank. January 2004 (has links) (PDF)
München, Techn. Universiẗat, Diss., 2004.
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SCARC ein verallgemeinertes Gebietszerlegungs-Mehrgitterkonzept auf Parallelrechnern /Kilian, Susanne. Unknown Date (has links) (PDF)
Universiẗat, Diss., 2002--Dortmund. / Gedr. Ausg. im Logos-Verl., Berlin.
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Penalized Least Squares Methoden mit stückweise polynomialen Funktionen zur Lösung von partiellen Differentialgleichungen / Penalized least squares methods with piecewise polynomial functions for solving partial differential equationsPechmann, Patrick R. January 2008 (has links) (PDF)
Das Hauptgebiet der Arbeit stellt die Approximation der Lösungen partieller Differentialgleichungen mit Dirichlet-Randbedingungen durch Splinefunktionen dar. Partielle Differentialgleichungen finden ihre Anwendung beispielsweise in Bereichen der Elektrostatik, der Elastizitätstheorie, der Strömungslehre sowie bei der Untersuchung der Ausbreitung von Wärme und Schall. Manche Approximationsaufgaben besitzen keine eindeutige Lösung. Durch Anwendung der Penalized Least Squares Methode wurde gezeigt, dass die Eindeutigkeit der gesuchten Lösung von gewissen Minimierungsaufgaben sichergestellt werden kann. Unter Umständen lässt sich sogar eine höhere Stabilität des numerischen Verfahrens gewinnen. Für die numerischen Betrachtungen wurde ein umfangreiches, effizientes C-Programm erstellt, welches die Grundlage zur Bestätigung der theoretischen Voraussagen mit den praktischen Anwendungen bildete. / This work focuses on approximating solutions of partial differential equations with Dirichlet boundary conditions by means of spline functions. The application of partial differential equations concerns the fields of electrostatics, elasticity, fluid flow as well as the analysis of the propagation of heat and sound. Some approximation problems do not have a unique solution. By applying the penalized least squares method it has been shown that uniqueness of the solution of a certain class of minimizing problems can be guaranteed. In some cases it is even possible to reach higher stability of the numerical method. For the numerical analysis we have developed an extensive and efficient C code. It serves as the basis to confirm theoretical predictions with practical applications.
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The Fourier-finite-element method with Nitsche-mortaringHeinrich, Bernd, Jung, Beate 01 September 2006 (has links) (PDF)
The paper deals with a combination of the
Fourier-finite-element method with the
Nitsche-finite-element method (as a mortar method).
The approach is applied to the Dirichlet problem
of the Poisson equation in three-dimensional
axisymmetric domains $\widehat\Omega$ with
non-axisymmetric data. The approximating Fourier
method yields a splitting of the 3D-problem into
2D-problems. For solving the 2D-problems on the
meridian plane $\Omega_a$,
the Nitsche-finite-element method with
non-matching meshes is applied. Some important
properties of the approximation scheme are
derived and the rate of convergence in some
$H^1$-like norm is proved to be of the type
${\mathcal O}(h+N^{-1})$ ($h$: mesh size on
$\Omega_a$, $N$: length of the Fourier sum) in
case of a regular solution of the boundary value
problem. Finally, some numerical results are
presented.
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Nitsche- and Fourier-finite-element method for the Poisson equation in axisymmetric domains with re-entrant edgesHeinrich, Bernd, Jung, Beate 11 September 2006 (has links) (PDF)
The paper deals with a combination of the Fourier
method with the Nitsche-finite-element method
(as a mortar method). The approach is applied to
the Dirichlet problem of the Poisson equation in
threedimensional axisymmetric domains with
reentrant edges generating singularities.
The approximating Fourier method yields a
splitting of the 3D problem into 2D problems
on the meridian plane of the given domain.
For solving the 2D problems bearing corner
singularities, the Nitsche finite-element
method with non-matching meshes and mesh
grading near reentrant corners is applied.
Using the explicit representation of singular
functions, the rate of convergence of the
Fourier-Nitsche-mortaring is estimated in some
$H^1$-like norm as well as in the $L_2$-norm.
Finally, some numerical results are presented.
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Induced charge computationSüzen, Mehmet Unknown Date (has links) (PDF)
Frankfurt (Main), Univ., Diss., 2009
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Nitsche- and Fourier-finite-element method for the Poisson equation in axisymmetric domains with re-entrant edgesHeinrich, Bernd, Jung, Beate 11 September 2006 (has links)
The paper deals with a combination of the Fourier
method with the Nitsche-finite-element method
(as a mortar method). The approach is applied to
the Dirichlet problem of the Poisson equation in
threedimensional axisymmetric domains with
reentrant edges generating singularities.
The approximating Fourier method yields a
splitting of the 3D problem into 2D problems
on the meridian plane of the given domain.
For solving the 2D problems bearing corner
singularities, the Nitsche finite-element
method with non-matching meshes and mesh
grading near reentrant corners is applied.
Using the explicit representation of singular
functions, the rate of convergence of the
Fourier-Nitsche-mortaring is estimated in some
$H^1$-like norm as well as in the $L_2$-norm.
Finally, some numerical results are presented.
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