An unfitted Nitsche method for incompressible fluid-structure interaction using overlapping meshes

We consider the extension of the Nitsche method to the case of fluid–structure interaction problems on unfitted meshes. We give a stability analysis for the space semi-discretized problem and show how this estimate may be used to derive optimal error estimates for smooth solutions,irrespectively of the mesh/interface intersection. We also discuss different strategies for the time discretization, using either fully implicit or explicit coupling (loosely coupled) schemes. Some numerical examples illustrate the theoretical discussion

Analysing children's accounts using discourse analysis

Discourse analytic approaches to research depart from understandings of the individual and of the relation between language and knowledge provided by positivist and post-positivist approaches. This chapter sets out to show what this might mean for studying children’s experiences through, for example, interview-based research, and how a discourse analytic approach may bring into play conceptual resources that are particularly valuable for research with children. First and foremost, discursive approaches highlight the interpretive nature of any research, not only that with children. As a consequence, they challenge the conventional distinction between data collection and analysis, question the status of research accounts and encourage us to question taken-for-granted assumptions about distinctions between adults and children. Hence our emphasis in this chapter is on the active and subjective involvement of researchers in hearing, interpreting and representing children’s ‘voices’

Towards measurement and verification of energy performance under the framework of the European directive for energy performance of buildings

Directive 2002/91/EC of the European Parliament and Council on the Energy Performance of Buildings has led to major developments in energy policies followed by the EU Member States. The national energy performance targets for the built environment are mostly rooted in the Building Regulations that are shaped by this Directive. Article 3 of this Directive requires a methodology to calculate energy performance of buildings under standardised operating conditions. Overwhelming evidence suggests that actual energy performance is often significantly higher than this standardised and theoretical performance. The risk is national energy saving targets may not be achieved in practice. The UK evidence for the education and office sectors is presented in this paper. A measurement and verification plan is proposed to compare actual energy performance of a building with its theoretical performance using calibrated thermal modelling. Consequently, the intended vs. actual energy performance can be established under identical operating conditions. This can help identify the shortcomings of construction process and building procurement. Once energy performance gap is determined with reasonable accuracy and root causes identified, effective measures could be adopted to remedy or offset this gap

A Proposal to Finance Long-Term Care Services through Medicare with an Income Tax Surcharge

Proposes expanding Medicare to cover comprehensive long-term care services, including home care and custodial nursing home care, and financing this expansion of benefits with a surcharge on federal income taxes

Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part II: hyperbolic equations.

In this paper we consider stabilized finite element methods for hyperbolic transport equations without coercivity. Abstract conditions for the convergence of the methods are introduced and these conditions are shown to hold for three different stabilized methods: the Galerkin least squares method, the continuous interior penalty method, and the discontinuous Galerkin method. We consider both the standard stabilization methods and the optimization-based method introduced in [E. Burman, SIAM J. Sci. Comput., 35 (2013), pp. A2752--A2780]. The main idea of the latter is to write the stabilized method in an optimization framework and select the discrete function for which a certain cost functional, in our case the stabilization term, is minimized. Some numerical examples illustrate the theoretical investigations. Read More: http://epubs.siam.org/doi/abs/10.1137/13093166

Projection Stabilization of Lagrange Multipliers for the Imposition of Constraints on Interfaces and Boundaries

Projection stabilization applied to general Lagrange multiplier finite element methods is introduced and analyzed in an abstract framework. We then consider some applications of the stabilized methods: (i) the weak imposition of boundary conditions, (ii) multiphysics coupling on unfitted meshes, (iii) a new interpretation of the classical residual stabilized Lagrange multiplier method introduced in Barbosa and Hughes, Comput Methods Appl Mech Eng 85 (1991), 109–128. © 2013 The Authors. Numerical Methods for Partial Differential Equations Published by Wiley Periodicals, Inc. 30: 567–592, 201

Robust error estimates for stabilized finite element approximations of the two dimensional Navier-Stokes' equations at high Reynolds number

We consider error estimates for stabilized finite element approximations of the two-dimensional Navier–Stokes’ equations on the unit square with periodic boundary conditions. The estimates for the vorticity are obtained in a weak norm that can be related to the norms of filtered quantities. L2-norm estimates are obtained for the velocities. Under the assumption of the existence of a certain decomposition of the solution, into large eddies and small fine scale fluctuations, the constants of the estimates are proven to be independent of the Reynolds number. Instead they depend on the L∞-norm of the initial vorticity and an exponential with factor proportional to the L∞-norm of the gradient of the large eddies. The main error estimates are on a posteriori form, but for certain stabilized methods the residuals may be upper bounded uniformly, leading to robust a priori error estimates

Using temporal distributions of transient events to characterize cosmological source populations

The brightest events in a time series of cosmological transients obey an observation time dependence which is often overlooked. This dependence can be exploited to probe the global properties of electromagnetic and gravitational wave transients (Howell et al. 2007a, Coward & Burman 2005). We describe a new relation based on a peak flux--observation time distribution and show that it is invariant to the luminosity distribution of the sources (Howell et al. 2007b). Applying this relation, in combination with a new data analysis filter, to \emph{Swift} gamma-ray burst data, we demonstrate that it can constrain their rate density.Comment: published in proceedings of FRONTIERS OF FUNDAMENTAL AND COMPUTATIONAL PHYSICS: 10th International Symposium, AIP,1246,203, (2010

A stabilized nonconforming finite element method for the elliptic Cauchy problem

In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data on the estimates is investigated. The recently derived framework from \cite{Bu13,Bu14} is extended to include the case of nonconforming approximation spaces and we show that the use of such spaces allows us to reduce the amount of stabilization necessary for convergence, even in the case of ill-posed problems

A monotonicity preserving, nonlinear, finite element upwind method for the transport equation

We propose a simple upwind finite element method that is monotonicity preserving and weakly consistent of order O(h3/2). The scheme is nonlinear, but since an explicit time integration method is used the added cost due to the nonlinearity is not prohibitive. We prove the monotonicity preserving property for the forward Euler method and for a second order Runge–Kutta method. The convergence properties of the Runge–Kutta finite element method are verified on a numerical example