1,921 research outputs found

    Dancksagung || Für das bitter leiden || vnd sterben Jesu || Christi.|| Mit angehengtem bericht von || dem Abendmal des Herrn.|| Vnd wes sich ein Christen vn=||ter schrecklichem Wetter vnd || harten Donnerschlegen || trösten sol.|| Gestellet durch || M. Stephanum Praetorium.|| Anno salutis 1582.|| 25 Martij.||

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    Vorlageform des Erscheinungsvermerks: [Uelzen: Michael Kröner 1582]Praetorius, Stephan: Bericht von dem Abendmahl des Herrn. (VD16 P 4665)Praetorius, Stephan: Wes sich ein Christen unter schrecklichem Wetter und harten Donnerschlägen trösten soll. (VD16 P 4682

    Different Strategies for the Adaptive FEM-BEM Coupling (Supervisor: M. Aurada, D. Praetorius)

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    For a nonlinear transmission problem with the 2D Laplacian, we consider three different FEM-BEM coupling strategies, namely o the symmetric coupling due to Costabel, o the Johnson-Nedelec coupling, o the Bielak-MacCamy coupling. we recall the continuous and discrete formulations and collect the mathmatical results available in the current literature. For the symmetric coupling, we recall two adaptive strategies steered by the residual error estimator from [Carstensen, Stephan 1995] and the recently introduced (h-h/2)-type error estimator from [Aurada, Feischl, Praetorius 2010]. Numerical experiments conclude the work

    The saturation assumption yields optimal convergence of two-level adaptive BEM

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    We consider the convergence of adaptive BEM for weakly-singular and hypersingular integral equations associated with the Laplacian and the Helmholtz operator in 2D and 3D. The local mesh-refinement is driven by some two-level error estimator. We show that the adaptive algorithm drives the underlying error estimates to zero. Moreover, we prove that the saturation assumption already implies linear convergence of the error with optimal algebraic rates

    Energy Norm Based A Posteriori Error Estimation for Boundary Element Methods in Two Dimensions

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    A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary element computations. We analyze the mathematical relation between the h-h/2-error estimator from [Ferraz-Leite, Praetorius 2009], the two-level error estimator from [Mund, Stephan, Weisse 1998], and the averaging error estimator from [Carstensen, Praetorius 2006]. We essentially show that all of these are equivalent, and we extend the analysis of [Mund, Stephan, Weisse 1998] to cover adaptive mesh-refinement. Therefore, all error estimators give lower bounds for the Galerkin error, whereas upper bounds depend crucially on the saturation assumption. As model examples, we consider first-kind integral equations in 2D with weakly singular integral kernel

    Energy Norm Based A Posteriori Error Estimation for Boundary Element Methods in Two Dimensions

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    A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary element computations. We analyze the mathematical relation between the h-h/2-error estimator from [Ferraz-Leite, Praetorius 2007], the two-level error estimator from [Mund, Stephan, Weisse 1998], and the averaging error estimator from [Carstensen, Praetorius 2005]. We essentially show that all of these are equivalent, and we extend the analysis of [Mund, Stephan, Weisse 1998] to cover adaptive mesh-refinement. Therefore, all error estimators give lower bounds for the Galerkin error, whereas upper bounds depend crucially on the saturation assumption. As model example serve first-kind integral equations in 2D with weakly singular integral kernel

    Ask questions, get sales : close the deak and create long-term relationships / Stephan Schiffman.

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    Includes index.v, 168 pages ;In Ask Questions, Get Sales, the author and sales guru Stephan Schiffman helps readers boost their careers to the gold-medal level by teaching them how to strengthen their questioning skills during the sales process. The premise is simple yet effective: In order to be successful, salespeople need to change their mindset from "need-orientated" to "do-orientated". The message of the book centers around six core "do" questions: What do you do? How do you do it? When and where do you do it? Why do you do it that way? Who do you do it with? How can we help you do it better? With this indispensable guide in their briefcase, salespeople will have information at the ready to score big sales over the short term and the long term

    Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D

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    A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary element computations. For hypersingular integral equations in 2D with positive-order Sobolev space, we analyze the mathematical relation between the (h− h/2)-error estimator from [Ferraz-Leite, Praetorius 2008], the two-level error estimator from [Maischak, Mund, Stephan 1997], and the averaging error estimator from [Carstensen, Praetorius 2007]. All of these a posteriori error estimators are simple in the following sense: First, the numerical analysis can be done within the same mathematical framework, namely localization techniques for the energy norm. Second, there is almost no implementational overhead for the realization
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