Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization

We consider a finite element method (FEM) with arbitrary polynomial degree for nonlinear monotone elliptic problems. Using a linear elliptic projection, we first give a new short proof of the optimal convergence rate of the FEM in the L2 norm. We then derive optimal a priori error estimates in the H 1 and L2 norm for a FEM with variational crimes due to numerical integration. As an application we derive a priori error estimates for a numerical homogenization method applied to nonlinear monotone elliptic problems

Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales

A discontinuous Galerkin finite element heterogeneous multiscale method is proposed for advectiondiffusion problems with highly oscillatory coefficients. The method is based on a coupling of a discontinuous Galerkin discretization for an effective advection-diffusion problem on a macroscopic mesh, whose a priori unknown data are recovered from micro finite element calculations on sampling domains within each macro element. The computational work involved is independent of the high oscillations in the problem at the smallest scale. The stability of our method (depending on both macro and micro mesh sizes) is established for both diffusion dominated and advection dominated regimes without any assumptions about the type of heterogeneities in the data. Fully discrete a priori error bounds are derived for locally periodic data. Numerical experiments confirm the theoretical error estimates

MATHICSE Technical Report : Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems

We propose a multiscale method based on a finite element heterogeneous multiscale method (in space) and the implicit Euler integrator (in time) to solve nonlinear monotone parabolic problems with multiple scales due to spatial heterogeneities varying rapidly at a microscopic scale. The multiscale method approximates the solution at the scale of interest at computational cost independent of the small scale by performing numerical upscaling (coupling of macro and micro finite element methods). Optimal a priori error estimates in the L^2(H^1) and C^0(L^2) norm are derived taking into account the error due to time discretization as well as macro and micro spatial discretizations. Further, we present numerical simulations to illustrate the theoretical error estimates and the applicability of the multiscale method to practical problems

Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems

We introduce and analyze an efficient numerical homogenization method for a class of nonlinear parabolic problems of monotone type in highly oscillatory media. The new scheme avoids costly Newton iterations and is linear at both the macroscopic and the microscopic scales. It can be interpreted as a linearized version of a standard nonlinear homogenization method. We prove the stability of the method and derive optimal a priori error estimates which are fully discrete in time and space. Numerical experiments confirm the error bounds and illustrate the efficiency of the methodfor various nonlinear problems

Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects

We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained

Accuracy, realism and general applicability of European forest models

Forest models are instrumental for understanding and projecting the impact of climate change on forests. A considerable number of forest models have been developed in the last decades. However, few systematic and comprehensive model comparisons have been performed in Europe that combine an evaluation of modelled carbon and water fluxes and forest structure. We evaluate 13 widely used, state-of-the-art, stand-scale forest models against field measurements of forest structure and eddy-covariance data of carbon and water fluxes over multiple decades across an environmental gradient at nine typical European forest stands. We test the models\u27 performance in three dimensions: accuracy of local predictions (agreement of modelled and observed annual data), realism of environmental responses (agreement of modelled and observed responses of daily gross primary productivity to temperature, radiation and vapour pressure deficit) and general applicability (proportion of European tree species covered). We find that multiple models are available that excel according to our three dimensions of model performance. For the accuracy of local predictions, variables related to forest structure have lower random and systematic errors than annual carbon and water flux variables. Moreover, the multi-model ensemble mean provided overall more realistic daily productivity responses to environmental drivers across all sites than any single individual model. The general applicability of the models is high, as almost all models are currently able to cover Europe\u27s common tree species. We show that forest models complement each other in their response to environmental drivers and that there are several cases in which individual models outperform the model ensemble. Our framework provides a first step to capturing essential differences between forest models that go beyond the most commonly used accuracy of predictions. Overall, this study provides a point of reference for future model work aimed at predicting climate impacts and supporting climate mitigation and adaptation measures in forests

Accuracy, realism and general applicability of European forest models

Forest models are instrumental for understanding and projecting the impact of climate change on forests. A considerable number of forest models have been developed in the last decades. However, few systematic and comprehensive model comparisons have been performed in Europe that combine an evaluation of modelled carbon and water fluxes and forest structure. We evaluate 13 widely used, state-of-the-art, stand-scale forest models against field measurements of forest structure and eddy-covariance data of carbon and water fluxes over multiple decades across an environmental gradient at nine typical European forest stands. We test the models' performance in three dimensions: accuracy of local predictions (agreement of modelled and observed annual data), realism of environmental responses (agreement of modelled and observed responses of daily gross primary productivity to temperature, radiation and vapour pressure deficit) and general applicability (proportion of European tree species covered). We find that multiple models are available that excel according to our three dimensions of model performance. For the accuracy of local predictions, variables related to forest structure have lower random and systematic errors than annual carbon and water flux variables. Moreover, the multi-model ensemble mean provided overall more realistic daily productivity responses to environmental drivers across all sites than any single individual model. The general applicability of the models is high, as almost all models are currently able to cover Europe's common tree species. We show that forest models complement each other in their response to environmental drivers and that there are several cases in which individual models outperform the model ensemble. Our framework provides a first step to capturing essential differences between forest models that go beyond the most commonly used accuracy of predictions. Overall, this study provides a point of reference for future model work aimed at predicting climate impacts and supporting climate mitigation and adaptation measures in forests.Peer reviewe

Consensus Statement on Bone Conduction Devices and Active Middle Ear Implants in Conductive and Mixed Hearing Loss

Nowadays, several options are available to treat patients with conductive or mixed hearing loss. Whenever surgical intervention is not possible or contra-indicated, and amplification by a conventional hearing device (e.g., behind-the-ear device) is not feasible, then implantable hearing devices are an indispensable next option. Implantable bone-conduction devices and middle-ear implants have advantages but also limitations concerning complexity/invasiveness of the surgery, medical complications, and effectiveness. To counsel the patient, the clinician should have a good overview of the options with regard to safety and reliability as well as unequivocal technical performance data. The present consensus document is the outcome of an extensive iterative process including ENT specialists, audiologists, health-policy scientists, and representatives/technicians of the main companies in this field. This document should provide a first framework for procedures and technical characterization to enhance effective communication between these stakeholders, improving health care

Mycobacterial PIMs Inhibit Host Inflammatory Responses through CD14-Dependent and CD14-Independent Mechanisms

Mycobacteria develop strategies to evade the host immune system. Among them, mycobacterial LAM or PIMs inhibit the expression of pro-inflammatory cytokines by activated macrophages. Here, using synthetic PIM analogues, we analyzed the mode of action of PIM anti-inflammatory effects. Synthetic PIM1 isomer and PIM2 mimetic potently inhibit TNF and IL-12 p40 expression induced by TLR2 or TLR4 pathways, but not by TLR9, in murine macrophages. We show inhibition of LPS binding to TLR4/MD2/CD14 expressing HEK cells by PIM1 and PIM2 analogues. More specifically, the binding of LPS to CD14 was inhibited by PIM1 and PIM2 analogues. CD14 was dispensable for PIM1 and PIM2 analogues functional inhibition of TLR2 agonists induced TNF, as shown in CD14-deficient macrophages. The use of rough-LPS, that stimulates TLR4 pathway independently of CD14, allowed to discriminate between CD14-dependent and CD14-independent anti-inflammatory effects of PIMs on LPS-induced macrophage responses. PIM1 and PIM2 analogues inhibited LPS-induced TNF release by a CD14-dependent pathway, while IL-12 p40 inhibition was CD14-independent, suggesting that PIMs have multifold inhibitory effects on the TLR4 signalling pathway

Preventive medicine of von Hippel-Lindau disease-associated pancreatic neuroendocrine tumors

Pancreatic neuroendocrine tumors (PanNETs) are rare in von Hippel-Lindau disease (VHL) but cause serious morbidity and mortality. Management guidelines for VHL-PanNETs continue to be based on limited evidence, and survival data to guide surgical management are lacking. We established the European-American-Asian-VHL-PanNET-Registry to assess data for risks for metastases, survival and long-term outcomes to provide best management recommendations. Of 2330 VHL patients, 273 had a total of 484 PanNETs. Median age at diagnosis of PanNET was 35 years (range 10-75). Fifty-five (20%) patients had metastatic PanNETs. Metastatic PanNETs were significantly larger (median size 5 vs 2\u2009cm; P\u20091.5\u2009cm in diameter were operated. Ten-year survival was significantly longer in operated vs non-operated patients, in particular for PanNETs <2.8\u2009cm vs 652.8\u2009cm (94% vs 85% by 10 years; P\u2009=\u20090.020; 80% vs 50% at 10 years; P\u2009=\u20090.030). This study demonstrates that patients with PanNET approaching the cut-off diameter of 2.8\u2009cm should be operated. Mutations in exon 3, especially of codons 161/167 are at enhanced risk for metastatic PanNETs. Survival is significantly longer in operated non-metastatic VHL-PanNETs