Austrian Academy of Sciences

Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschaften
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    Preliminaries. Orea|The Ancient Throne Oriental and European Archaeology Volume 14|

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    Postbyzantinische Epigramme in inschriftlicher Überlieferung (PBEiÜ)

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    An a-priori error analysis for discontinuous Lagrangian finite elements applied to nonconforming dual-mixed formulations: Poisson and Stokes problems. ETNA - Electronic Transactions on Numerical Analysis

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    In this paper, we discuss the well-posedness of a mixed discontinuous Galerkin (DG) scheme for the Poisson and Stokes problems in 2D, considering only piecewise Lagrangian finite elements. The complication here lies in the fact that the classical Babuška-Brezzi theory is difficult to verify for low-order finite elements, so we proceed in a non-standard way. First, we prove uniqueness, and then we apply a discrete version of Fredholm's alternative theorem to ensure existence. The a-priori error analysis is done by introducing suitable projections of the exact solution. As a result, we prove that the method is convergent, and, under standard additional regularity assumptions on the exact solution, the optimal rate of convergence of the method is guaranteed

    Primal-dual block-proximal splitting for a class of non-convex problems. ETNA - Electronic Transactions on Numerical Analysis

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    We develop block structure-adapted primal-dual algorithms for non-convexnon-smooth optimisation problems, whose objectives can be written as compositionsG(x)+F(K(x))G(x)+F(K(x)) of non-smooth block-separable convex functions GG and FF with anonlinear Lipschitz-differentiable operator KK. Our methods are refinements ofthe nonlinear primal-dual proximal splitting method for such problems withoutthe block structure, which itself is based on the primal-dual proximal splittingmethod of Chambolle and Pock for convex problems. We propose individual steplength parameters and acceleration rules for each of the primal and dual blocksof the problem. This allows them to convergence faster by adapting to thestructure of the problem. For the squared distance of the iterates to a criticalpoint, we show local O(1/N)O(1/N), O(1/N2)O(1/N^2), and linear rates under varyingconditions and choices of the step length parameters. Finally, we demonstrate the performance of the methods for the practical inverseproblems of diffusion tensor imaging and electrical impedance tomography

    Großbauer, Ludwig Franz

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    * 19.8.1840 St. Egidi in Windischbüheln/St (Šentilj/SLO), † 18.3.1907 Wien. Lehrer, Sänger (Tenor), Komponist

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