Adaptive discontinuous Galerkin approximations to fourth order parabolic problems

An adaptive algorithm, based on residual type a posteriori indicators of errors measured in $L^{\infty}(L^2)$ and $L^2(L^2)$ norms, for a numerical scheme consisting of implicit Euler method in time and discontinuous Galerkin method in space for linear parabolic fourth order problems is presented. The a posteriori analysis is performed for convex domains in two and three space dimensions for local spatial polynomial degrees $r\ge 2$. The a posteriori estimates are then used within an adaptive algorithm, highlighting their relevance in practical computations, which results into substantial reduction of computational effort

An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems

A posteriori error control for discontinuous Galerkin methods for parabolic problems

We derive energy-norm a posteriori error bounds for an Euler time-stepping method combined with various spatial discontinuous Galerkin schemes for linear parabolic problems. For accessibility, we address first the spatially semidiscrete case, and then move to the fully discrete scheme by introducing the implicit Euler time-stepping. All results are presented in an abstract setting and then illustrated with particular applications. This enables the error bounds to hold for a variety of discontinuous Galerkin methods, provided that energy-norm a posteriori error bounds for the corresponding elliptic problem are available. To illustrate the method, we apply it to the interior penalty discontinuous Galerkin method, which requires the derivation of novel a posteriori error bounds. For the analysis of the time-dependent problems we use the elliptic reconstruction technique and we deal with the nonconforming part of the error by deriving appropriate computable a posteriori bounds for it.Comment: 6 figure

International intermediaries: A systematic literature review and research agenda

Intermediaries such as trading companies, agents and merchants have played a key role in international business for centuries. Despite the growing importance of understanding the phenomenon of intermediaries, there are misperceptions and confusions regarding the concept and value of intermediaries, which result in disconnected and fragmented research findings. This study – based on an analysis of 101 articles published between 1985 and 2021 – aims to synthesise the conceptual developments and provide a more integrated understanding of both sourcing and trading intermediaries whose activities extend across national borders. The findings help to pave the way for further academic research by highlighting what we currently know and do not know about intermediaries, outlining the theoretically grounded research agenda for each of the three identified themes: (1) What are intermediaries? (2) When should intermediaries be used? and (3) How do intermediaries work and develop? The study shows that despite decades of research on this topic, the literature to date has been limited and scattered. Researchers are encouraged to consider the role of intermediaries in a bigger picture where intermediated exchanges exist not only in dyadic relationships, but also in triads or even in broader webs of networks

Visualizations relevant to the user by multi-view latent variable factorization

A main goal of data visualization is to find, from among all the available alternatives, mappings to the 2D/3D display which are relevant to the user. Assuming user interaction data, or other auxiliary data about the items or their relationships, the goal is to identify which aspects in the primary data support the user's input and, equally importantly, which aspects of the user's potentially noisy input have support in the primary data. For solving the problem, we introduce a multi-view embedding in which a latent factorization identifies which aspects in the two data views (primary data and user data) are related and which are specific to only one of them. The factorization is a generative model in which the display is parameterized as a part of the factorization and the other factors explain away the aspects not expressible in a two-dimensional display. Functioning of the model is demonstrated on several data sets

Microwave response of an NS ring coupled to a superconducting resonator

A long phase coherent normal (N) wire between superconductors (S) is characterized by a dense phase dependent Andreev spectrum . We probe this spectrum in a high frequency phase biased configuration, by coupling an NS ring to a multimode superconducting resonator. We detect a dc flux and frequency dependent response whose dissipative and non dissipative components are related by a simple Debye relaxation law with a characteristic time of the order of the diffusion time through the N part of the ring. The flux dependence exhibits $h/2e$ periodic oscillations with a large harmonics content at temperatures where the Josephson current is purely sinusoidal. This is explained considering that the populations of the Andreev levels are frozen on the time-scale of the experiments.Comment: 5 pages,4 figure

Mesangial cells organize the glomerular capillaries by adhering to the G domain of laminin α5 in the glomerular basement membrane

In developing glomeruli, laminin α5 replaces laminin α1 in the glomerular basement membrane (GBM) at the capillary loop stage, a transition required for glomerulogenesis. To investigate domain-specific functions of laminin α5 during glomerulogenesis, we produced transgenic mice that express a chimeric laminin composed of laminin α5 domains VI through I fused to the human laminin α1 globular (G) domain, designated Mr51. Transgene-derived protein accumulated in many basement membranes, including the developing GBM. When bred onto the Lama5 −/− background, Mr51 supported GBM formation, preventing the breakdown that normally occurs in Lama5 −/− glomeruli. In addition, podocytes exhibited their typical arrangement in a single cell layer epithelium adjacent to the GBM, but convolution of glomerular capillaries did not occur. Instead, capillaries were distended and exhibited a ballooned appearance, a phenotype similar to that observed in the total absence of mesangial cells. However, here the phenotype could be attributed to the lack of mesangial cell adhesion to the GBM, suggesting that the G domain of laminin α5 is essential for this adhesion. Analysis of an additional chimeric transgene allowed us to narrow the region of the α5 G domain essential for mesangial cell adhesion to α5LG3-5. Finally, in vitro studies showed that integrin α3β1 and the Lutheran glycoprotein mediate adhesion of mesangial cells to laminin α5. Our results elucidate a mechanism whereby mesangial cells organize the glomerular capillaries by adhering to the G domain of laminin α5 in the GBM

An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems