Error analysis for an ALE evolving surface finite element method

We consider an arbitrary Lagrangian–Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a moving surface. We describe the method, prove optimal order error bounds and present numerical simulations that agree with the theoretical results

A fully discrete evolving surface finite element method

In this paper we consider a time discrete evolving surface finite element method for the advection and diffusion of a conserved scalar quantity on a moving surface. In earlier papers using a suitable variational formulation in time dependent Sobolev space we proposed and analyzed a finite element method using surface finite elements on evolving triangulated surfaces [IMA J. Numer Anal., 25 (2007), pp. 385--407; Math. Comp., to appear]. Optimal order L2(Γ(t)) and H1(Γ(t)) error bounds were proved for linear finite elements. In this work we prove optimal order error bounds for a backward Euler time discretization

Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces

Convergence results are shown for full discretizations of quasilinear parabolic partial differential equations on evolving surfaces. As a semidiscretization in space the evolving surface finite element method is considered, using a regularity result of a generalized Ritz map, optimal order error estimates for the spatial discretization is shown. Combining this with the stability results for Runge--Kutta and BDF time integrators, we obtain convergence results for the fully discrete problems.Comment: -. arXiv admin note: text overlap with arXiv:1410.048

Overview of meteorological inputs to NASP

An overview of meteorological systems for forecasting flight conditions is presented. The types of equipment used to gather the information used to prepare pilot briefings and in flight advisories is described. Possible improvements to the systems are classified as short term or long term

L² -estimates for the evolving surface finite element method

In this paper we consider the evolving surface finite element method for the advection and diffusion of a conserved scalar quantity on a moving surface. In an earlier paper using a suitable variational formulation in time dependent Sobolev space we proposed and analysed a finite element method using surface finite elements on evolving triangulated surfaces. An optimal order H¹ -error bound was proved for linear finite elements. In this work we prove the optimal error bound in L² (Γ(t)) uniformly in time

Finite element methods for surface PDEs

In this article we consider finite element methods for approximating the solution of partial differential equations on surfaces. We focus on surface finite elements on triangulated surfaces, implicit surface methods using level set descriptions of the surface, unfitted finite element methods and diffuse interface methods. In order to formulate the methods we present the necessary geometric analysis and, in the context of evolving surfaces, the necessary transport formulae. A wide variety of equations and applications are covered. Some ideas of the numerical analysis are presented along with illustrative numerical examples

The prognostic value of myocardial perfusion scintigraphy compared to coronary angiography in women with positive stress test results

BACKGROUND: Modern diagnostic strategy in coronary arterydisease (CAD) makes it necessary not only to establish a diagnosisbut also to assess the cardiovascular risk. It is not clearwhich strategy should be followed in the case of women withpositive ECG stress test results to assess prognosis and startappropriate diagnostics and treatment.The aim of the study was to assess the prognostic value ofmyocardial perfusion scintigraphy in comparison with coronaryangiography in women suspected of CAD and with positive ECGstress test results.MATERIAL AND METHODS: The study population comprised115 women (mean age 58.08 ± 8.8 years) suspected of CAD, witha history of chest pain and positive stress test results, who underwent myocardial perfusion scintigraphy. In 58 women coronaryangiography was performed as the next step of the diagnosticprocedure. All the patients were interviewed and had a physicalexamination, including the assessment of the cardiovascularrisk in accordance with the SCORE (Systematic Coronary RiskEvaluation) scale and the probability of CAD (POST-TEST) inaccordance with the ESC guidelines. The gated single photonemission computed tomography (GSPECT) with Tc-99m-MIBIwas considered positive if moderate perfusion changes wereobserved in at least two segments or severe reversible perfusiondisorders were found, regardless of the number of involved segments.The degree of coronary stenosis was assessed visuallyand changes greater than 50% stenosis of the luminal diameterwere considered haemodynamically significant.RESULTS: The evaluation period covered 43.2 ± 30.8 monthson average. The sensitivity of myocardial perfusion scintigraphyagainst cardiovascular events was 100% and the sensitivity ofcoronary angiography was 92.3%. The specificity was 93.1%and 88.9% respectively.The PPV of scintigraphy for cardiovascular events was 65% and ofcoronary angiography was 70.6%. The NPV was 100% and 97.6%respectively. The accuracy of myocardial perfusion scintigraphy forcardiovascular events was 93.9% and the accuracy of coronaryangiography for cardiovascular events was 89.7%. The survivalanalysis confirmed the high prognostic value of SPECT and coronaryangiography. However, if compared, myocardial perfusionscintigraphy was a better predictor of survival without cardiovascularevents than coronary angiography was (c2 = 9.39, p < 0.01).The most important factors in assessing the cardiovascular riskin the study population included: positive result of myocardialperfusion scintigraphy, positive result of coronary angiography,and high SCORE and high POST-TEST values.CONCLUSIONS: Myocardial perfusion scintigraphy is superiorto coronary angiography in the prediction of necessary revascularisation procedures in women suspected of coronary arterydisease and with positive stress test results

Modelling cell motility and chemotaxis with evolving surface finite elements

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/maskae/CV_Warwick/Chemotaxis.html

Projected finite elements for systems of reaction-diffusion equations on closed evolving spheroidal surfaces

The focus of this article is to present the projected finite element method for solving systems of reaction-diffusion equations on evolving closed spheroidal surfaces with applications to pattern formation. The advantages of the projected finite element method are that it is easy to implement and that it provides a conforming finite element discretization which is ``logically'' rectangular. Furthermore, the surface is not approximated but described exactly through the projection. The surface evolution law is incorporated into the projection operator resulting in a time-dependent operator. The time-dependent projection operator is composed of the radial projection with a Lipschitz continuous mapping. The projection operator is used to generate the surface mesh whose connectivity remains constant during the evolution of the surface. To illustrate the methodology several numerical experiments are exhibited for different surface evolution laws such as uniform isotropic (linear, logistic and exponential), anisotropic, and concentration-driven. This numerical methodology allows us to study new reaction-kinetics that only give rise to patterning in the presence of surface evolution such as the activator-activator and short-range inhibition; long-range activation