Convergence analysis for an exponentially fitted finite volume method
New results concerning the DWR method for some nonconforming FEM
This paper presents a unified framework for the dual-weighted residual (DWR) method for a class of nonconforming FEM. Our approach is based on a modification of the dual problem and uses various ideas from literature which are combined in a new manner. The results are new error identities for some nonconforming FEM. Additionally, a posteriori error estimates with respect to the discrete -seminorm are derived.
About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the Poisson equation
The starting point of the analysis in this paper is the following situation: “In a bounded domain in , let a finite set of points be given. A triangulation of that domain has to be found, whose vertices are the given points and which is ‘suitable’ for the linear conforming Finite Element Method (FEM).” The result of this paper is that for the discrete Poisson equation and under some weak additional assumptions, only the use of Delaunay triangulations preserves the maximum principle.
Explizite Konstruktion von linearen Mehrschrittblockverfahren
In der vorliegenden Arbeit wird für lineare Mehrschrittblock verfahren zur numerischen Lösung von Anfangswertaufgaben eine explizite Konstruktionsmöglichkeit angegeben. Sie ermöglicht es, zu einem gegebenen Stabilitätspolynom ohne Lösung eines linearen Gleichungssystems die Koefizienten des zugehörigen Blockverfahrens zu berechnen.
Erweiterung des -Stabilitätsbegriffes auf die Klasse der linearen Mehrschrittblockverfahren.
In der vorliegenden Arbeit wird der -Stabilitätsbegriff von Dahlquist, der die Grundlage für Stabilitätsuntersuchungen bei linearen Mehrschrittverfahren zur Lösung nichtlinearet Anfangswertaufgaben bildet, auf die Klasse der linearen Mehrschrittblockverfahren übertragen. Es wird nachgewiesen, das Blockverfahren, die in diesem Sinne stabil sind, höchstens die Konsistenzordnung 2 haben können.
Convergence analysis for an exponentially fitted Finite Volume Method
The paper is devoted to the convergence analysis of a well-known cell-centered Finite Volume Method (FVM) for a convection-diffusion problem in . This FVM is based on Voronoi boxes and exponential fitting. To prove the convergence of the FVM, we use a new nonconforming Petrov-Galerkin Finite Element Method (FEM) for which the system of linear equations coincides completely with that of the FVM. Thus, by proving convergence properties of the FEM we obtain similar ones for the FVM. For the error...
A comparison of four- and five-point difference approximations for stabilizing the one-dimensional stationary convection-diffusion equation.
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