Dawn singing in Brown Creeper (Certhia americana)

The dawn chorus of birds is an impressive display in which many individuals of a variety of species sing concurrently before sunrise. Brown Creeper (Certhia americana) is a small passerine bird that has not been well studied and is thought not to sing during the dawn chorus. Here, we used automated recordings to analyze Brown Creeper singing during the 2015–2017 breeding seasons from April through August in order to identify patterns in the timing and quantity of singing. We found that Brown Creepers did sing before sunrise, most often between April and early June and then more sporadically through mid July. We did not find any seasonal changes in song rates before sunrise, but we did find non-linear seasonal trends in both the timing and total duration of dawn singing bouts. Dawn choruses began earlier and lasted longer from April through mid June after which they began later and became shorter. Our results highlight the benefit of using automated recording techniques to study natural history of difficult to study species and add to our understanding of Brown Creeper natural history

A-posteriori error estimates for discontinuous galerkin approximations of second order elliptic problems

Using the weighted residual formulation we derive a-posteriori estimates for Discontinuous Galerkin approximations of second order elliptic problems in mixed form. We show that our approach allows to include in a unified way all the methods presented so far in the literature

A relaxation procedure for domain decomposition methods using finite elements

We present the convergence analysis of a new domain decomposition technique for finite element approximations. This technique was introduced in [11] and is based on an iterative procedure among subdomains in which transmission conditions at interfaces are taken into account partly in one subdomain and partly in its adjacent. No global preconditioner is needed in the practice, but simply single-domain finite element solvers are required. An optimal strategy for an automatic selection of a relaxation parameter to be used at interface subdomains is indicated. Applications are given to both elliptic equations and incompressible Stokes equations. © 1989 Springer-Verlag

Discontinuous Galerkin methods for advection-diffusion-reaction problems

We apply the weighted-residual approach to derive discontinuous Galerkin formulations for advection-diffusion-reaction problems. We devise the basic ingredients to ensure stability and optimal error estimates in suitable norms, and propose two new methods

Virtual Element Methods for plate bending problems

We discuss the application of Virtual Elements to linear plate bending problems, in the Kirchhoff-Love formulation. As we shall see, in the Virtual Element environment the treatment of the C^1-continuity condition is much easier than for traditional Finite Elements. The main difference consists in the fact that traditional Finite Elements, for every element E and for every given set of degrees of freedom, require the use of a space of polynomials (or piecewise polynomials for composite elements) for which the given set of degrees of freedom is unisolvent. For Virtual Elements instead we only need unisolvence for a space of smooth functions that contains a subset made of polynomials (whose degree determines the accuracy). As we shall see the non-polynomial part of our local spaces does not need to be known in detail, and therefore the construction of the local stiffness matrix is simple, and can be done for much more general geometries

A quick tutorial on DG methods for elliptic problems

In this paper we recall a few basic definitions and results concerning the use of DG methods for elliptic problems. As examples we consider the Poisson problem and the linear elasticity problem. A hint on the nearly incompressible case is given, just to show one of the possible advantages of DG methods over continuous ones. At the end of the paper we recall some physical principles for linear elasticity problems, just to open the door towards possible new developments

Virtual Element and Discontinuous Galerkin Methods

Virtual Element Methods (VEM) are the latest evolution of the Mimetic Finite Difference Method, and can be considered to be more close to the Finite Element approach. They combine the ductility of mimetic finite differences for dealing with rather weird element geometries with the simplicity of implementation of Finite Elements. Moreover they make it possible to construct quite easily high-order and high-regularity approximations (and in this respect they represent a significant improvement with respect to both FE and MFD methods)