Finite element error analysis of wave equations with dynamic boundary conditions: L2L^2 estimates

$L^2$ norm error estimates of semi- and full discretisations, using bulk--surface finite elements and Runge--Kutta methods, of wave equations with dynamic boundary conditions are studied. The analysis resides on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed which fit into the abstract framework. For problems with velocity terms, or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than two. These can also be observed in the presented numerical experiments

A unified error analysis for spatial discretizations of wave-type equations with applications to dynamic boundary conditions

This thesis provides a unified framework for the error analysis of non-conforming space discretizations of linear wave equations in time-domain, which can be cast as symmetric hyperbolic systems or second-order wave equations. Such problems can be written as first-order evolution equations in Hilbert spaces with linear monotone operators. We employ semigroup theory for the well-posedness analysis and to obtain stability estimates for the space discretizations. To compare the finite dimensional approximations with the original solution, we use the concept of a lift from the discrete to the continuous space. Time integration with the Crank–Nicolson method is analyzed. In this framework, we derive a priori error bounds for the abstract space semi-discretization in terms of interpolation and discretization errors. These error bounds yield previously unkown convergence rates for isoparametric finite element discretizations of wave equations with dynamic boundary conditions in smooth domains. Moreover, our results allow to consider already investigated space discretizations in a unified way. Here it successfully reproduces known error bounds. Among the examples which we dicuss in this thesis are discontinuous Galerkin discretizations of Maxwell’s equations and finite elements with mass lumping for the scalar wave equation

Unified error analysis for non-conforming space discretizations ofwave-type equations

This paper provides a unified error analysis for non-conforming space discretizations of linear wave equations in time-domain. We propose a framework which studies wave equations as first-order evolution equations in Hilbert spaces and their space discretizations as differential equations in finite dimensional Hilbert spaces. A lift operator maps the semi-discrete solution from the approximation space to the continuous space. Our main results are a priori error bounds in terms of interpolation, data and conformity errors of the method. Such error bounds are the key to the systematic derivation of convergence rates for a large class of problems. To show that this approach significantly eases the proof of new convergence rates, we apply it to an isoparametric finite element discretization of the wave equation with acoustic boundary conditions in a smooth domain. Moreover, our results reproduce known convergence rates for already investigated conforming and non-conforming space discretizations in a concise and unified way. The examples discussed in this paper comprise discontinuous Galerkin discretizations of Maxwell’s equations and finite elements with mass lumping for the acoustic wave equation

Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates

$L^2$ error estimates of semi- and full discretisations of wave equations with dynamic boundary conditions are studied, using bulk–surface finite elements and Runge–Kutta methods. The analysis resides on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed within the abstract framework. For problems with velocity terms, or with acoustic boundary conditions we prove a spatial convergence order which is less than two. These can also be observed in the presented numerical experiments

Plant Nutrition and Fertilizer Management for Winter Wheat Production in the Blackland Prairie.

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Hospital Costs Related to Early Extubation after Infant Cardiac Surgery

Background The Pediatric Heart Network Collaborative Learning Study (PHN CLS) increased early extubation rates after infant Tetralogy of Fallot (TOF) and coarctation (CoA) repair across participating sites by implementing a clinical practice guideline (CPG). The impact of the CPG on hospital costs has not been studied. Methods PHN CLS clinical data were linked to cost data from Children’s Hospital Association by matching on indirect identifiers. Hospital costs were evaluated across active and control sites in the pre- and post-CPG periods using generalized linear mixed effects models. A difference-in-difference approach was used to assess whether changes in cost observed in active sites were beyond secular trends in control sites. Results Data were successfully linked on 410/428 (96%) of eligible patients from 4 active and 4 control sites. Mean adjusted cost/case for TOF repair was significantly reduced in the post-CPG period at active sites ($42,833 vs.$56,304, p<0.01) and unchanged at control sites ($47,007 vs.$46,476, p=0.91), with an overall cost reduction of 27% in active vs. control sites (p=0.03). Specific categories of cost reduced in the TOF cohort included clinical (-66%, p<0.01), pharmacy (-46%, p=0.04), lab (-44%, p<0.01), and imaging (-32%, p<0.01). There was no change in costs for CoA repair at active or control sites. Conclusions The early extubation CPG was associated with a reduction in hospital costs for infants undergoing repair of TOF, but not CoA repair. This CPG represents an opportunity to both optimize clinical outcome and reduce costs for certain infant cardiac surgeries

A clinical genetic method to identify mechanisms by which pain causes depression and anxiety

BACKGROUND: Pain patients are often depressed and anxious, and benefit less from psychotropic drugs than pain-free patients. We hypothesize that this partial resistance is due to the unique neurochemical contribution to mood by afferent pain projections through the spino-parabrachial-hypothalamic-amygdalar systems and their projections to other mood-mediating systems. New psychotropic drugs for pain patients might target molecules in such brain systems. We propose a method to prioritize molecular targets by studying polymorphic genes in cohorts of patients undergoing surgical procedures associated with a variable pain relief response. We seek molecules that show a significant statistical interaction between (1) the amount of surgical pain relief, and (2) the alleles of the gene, on depression and anxiety during the first postoperative year. RESULTS: We collected DNA from 280 patients with sciatica due to a lumbar disc herniation, 162 treated surgically and 118 non-surgically, who had been followed for 10 years in the Maine Lumbar Spine Study, a large, prospective, observational study. In patients whose pain was reduced >25% by surgery, symptoms of depression and anxiety, assessed with the SF-36 Mental Health Scale, improved briskly at the first postoperative measurement. In patients with little or no surgical pain reduction, mood scores stayed about the same on average. There was large inter-individual variability at each level of residual pain. Polymorphisms in three pre-specified pain-mood candidate genes, catechol-O-methyl transferase (COMT), serotonin transporter, and brain-derived neurotrophic factor (BDNF) were not associated with late postoperative mood or with a pain-gene interaction on mood. Although the sample size did not provide enough power to persuasively search through a larger number of genes, an exploratory survey of 25 other genes provides illustrations of pain-gene interactions on postoperative mood – the mu opioid receptor for short-term effects of acute sciatica on mood, and the galanin-2 receptor for effects of unrelieved post-discectomy pain on mood one year after surgery. CONCLUSION: Genomic analysis of longitudinal studies of pain, depression, and anxiety in patients undergoing pain-relieving surgery may help to identify molecules through which pain alters mood. Detection of alleles with modest-sized effects will require larger cohorts

Comparative methods in R hackathon

The R statistical analysis package has emerged as a popular platform for implementation of powerful comparative methods to understand the evolution of organismal traits and diversification. A hackathon was organized to bring together active R developers as well as end-users working on the integration of comparative phylogenetic methods within R to actively address issues of data exchange standards, code interoperability, usability, documentation quality, and the breadth of functionality for comparative methods available within R. Outcomes included a new base package for phylogenetic trees and data, a public wiki with tutorials and overviews of existing packages, code to allow Mesquite and R to interact, improvement of existing packages, and increased interaction within the community