L∞(L∞)L^\infty(L^\infty)-boundedness of DG(pp)-solutions for nonlinear conservation laws with boundary conditions

We prove the $L^\infty(L^\infty)$-boundedness of a higher-order shock-capturing streamline-diffusion DG-method based on polynomials of degree $p\geq 0$ for general scalar conservation laws. The estimate is given for the case of several space dimensions and for conservation laws with initial and boundary conditions

Interpolation, projection and hierarchical bases in discontinuous Galerkin methods

The paper presents results on piecewise polynomial approximations of tensor product type in Sobolev-Slobodecki spaces by various interpolation and projection techniques, on error estimates for quadrature rules and projection operators based on hierarchical bases, and on inverse inequalities. The main focus is directed to applications to discrete conservation laws

Form and function in hillslope hydrology : in situ imaging and characterization of flow-relevant structures

Thanks to Elly Karle and the Engler-BunteInstitute, KIT, for the IC measurements of bromide. We are grateful to Selina Baldauf, Marcel Delock, Razije Fiden, Barbara Herbstritt, Lisei Köhn, Jonas Lanz, Francois Nyobeu, Marvin Reich and Begona Lorente Sistiaga for their support in the lab and during fieldwork, as well as Markus Morgner and Jean Francois Iffly for technical support and Britta Kattenstroth for hydrometeorological data acquisition. Laurent Pfister and Jean-Francois Iffly from the Luxembourg Institute of Science and Technology (LIST) are acknowledged for organizing the permissions for the experiments. Moreover, we thank Markus Weiler (University of Freiburg) for his strong support during the planning of the hillslope experiment and the preparation of the manuscript. This study is part of the DFG-funded CAOS project “From Catchments as Organised Systems to Models based on Dynamic Functional Units” (FOR 1598). The manuscript was substantially improved based on the critical and constructive comments of the anonymous reviewers, Christian Stamm and Alexander Zimmermann, and the editor Ross Woods during the open review process, which is highly appreciated.Peer reviewedPublisher PD

Form and function in hillslope hydrology : Characterization of subsurface ow based on response observations

Acknowledgements. We are grateful to Marcel Delock, Lisei Köhn, and Marvin Reich for their support during fieldwork, as well as Markus Morgner and Jean Francois Iffly for technical support, Britta Kattenstroth for hydrometeorological data acquisition and isotope sampling, and Barbara Herbstritt and Begoña Lorente Sistiaga for laboratory work. Laurent Pfister and Jean-Francois Iffly from the Luxembourg Institute of Science and Technology (LIST) are acknowledged for organizing the permissions for the experiments and providing discharge data for Weierbach 1 and Colpach. We also want to thank Frauke K. Barthold and the two anonymous reviewers, whose thorough remarks greatly helped to improve the manuscript. This study is part of DFG-funded CAOS project “From Catchments as Organised Systems to Models based on Dynamic Functional Units” (FOR 1598). The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.Peer reviewedPublisher PD

A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity

The present work describes some extensions of an approach, originally developed by V.V. Yatsyk and the author, for the theoretical and numerical analysis of scattering and radiation effects on infinite plates with cubically polarized layers. The new aspects lie on the transition to more generally shaped, two- or three-dimensional objects, which no longer necessarily have to be represented in terms a Cartesian product of real intervals, to more general nonlinearities (including saturation) and the possibility of an efficient numerical approximation of the electromagnetic fields and derived quantities (such as energy, transmission coefficient, etc.). The paper advocates an approach that consists in transforming the original full-space problem for a nonlinear Helmholtz equation (as the simplest model) into an equivalent boundary-value problem on a bounded domain by means of a nonlocal Dirichlet-to-Neumann (DtN) operator. It is shown that the transformed problem is equivalent to the original one and can be solved uniquely under suitable conditions. Morever, the impact of the truncation of the DtN operator on the resulting solution is investigated, so that the way to the numerical solution by appropriate finite element methods is available

Review of German, Jew, Muslim, Gay: The Life and Times of Hugo Marcus By Marc David Baer.

When Hugo Marcus (1880–1966), a German Jewish gay author, philosopher, and activist, converted to Islam in 1925, he “did not know yet what significance the word ‘jihad’ would one day mean to [him]. For it also signifies the duty to leave the country that is under godless rule, even if in so doing one has to give up one’s homeland. In this sense,” he wrote retrospectively in 1951, “I have been on a pilgrimage for the last twelve years” (135). In a footnote to this quotation from Marcus’s unpublished manuscript, Marc David Baer, author of this fascinating, erudite, and unusual biography, clarifies Marcus’s probable confusion between the Islamic terms jihad (holy war) and hejira (exile, migration). Driven away from his homeland in 1939, Marcus interpreted his own life in the religious vocabulary of Islam. But, ascending to become one the most prominent Muslims in pre-war Berlin, he also interpreted Islam in the light of his own experiences, worldviews, and wishes: as a German Jewish gay man. Not only was Marcus assigned with the monumentally significant project of editing and annotating the Qur’an’s translation into German, aimed at rendering it accessible to non-Arab speakers (reminiscent of Martin Buber and Franz Rosenzweig’s project of the Hebrew Bible’s translation into German, which would be an interesting point of comparison), but he also published numerous articles discussing Islam and philosophy as well as homoerotic fiction with Islamic themes

Finite element solution of a radiation/propagation problem for a Helmholtz equation with a compactly supported nonlinearity

A finite element method for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model consists of a nonlinear Helmholtz equation that is reduced to a spherical domain. The (exemplary) finite element method is formed by Courant-type elements with curved facets at the boundary of the spherical computational domain. This method is examined for its well-posedness, in particular the validity of a discrete inf-sup condition of the modified sesquilinear form uniformly with respect to both the truncation and the mesh parameters is shown. Under suitable assumptions to the nonlinearities, a quasi-optimal error estimate is obtained. Finally, the satisfiability of the approximation property of the finite element space required for the solvability of a class of adjoint linear problems is discussed

Projection-Based 2.5D U-net Architecture for Fast Volumetric Segmentation

Convolutional neural networks are state-of-the-art for various segmentation tasks. While for 2D images these networks are also computationally efficient, 3D convolutions have huge storage requirements and require long training time. To overcome this issue, we introduce a network structure for volumetric data without 3D convolutional layers. The main idea is to include maximum intensity projections from different directions to transform the volumetric data to a sequence of images, where each image contains information of the full data. We then apply 2D convolutions to these projection images and lift them again to volumetric data using a trainable reconstruction algorithm.The proposed network architecture has less storage requirements than network structures using 3D convolutions. For a tested binary segmentation task, it even shows better performance than the 3D U-net and can be trained much faster.Comment: presented at the SAMPTA 2019 conferenc