One-dimensional piecewise-smooth discontinuous maps (maps with gaps) are known to have surprisingly rich dynamics, including periodic orbits with very high period and bifurcation diagrams showing period-adding or period-incrementing behavour. In this paper we study a new class of maps, which we refer to as regularised one-dimensional discontinuous maps, because they give very similar dynamics t...

The development of the notochord, perichordal sheath and vertebrae was studied in C57BL/6 and Danforth's short-tail (Sd) mutant mice on days 9-14 of gestation, using histochemical stains to detect possible extracellular matrix (ECM) components or precursors. Stains used were periodic-acid Schiff (PAS) after diastase treatment (glycoproteins, neutral polysaccharides) and alcian blue (glycosamino...

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (R...

Event-driven molecular dynamics simulations are carried out on two rigid-body systems which differ in the symmetry of their molecular mass distributions. First, simulations of methane in which the molecules interact via discontinuous potentials are compared with simulations in which the molecules interact through standard continuous Lennard-Jones potentials. It is shown that under similar condi...

In this paper we analyse the problem of computing eigenvalues and eigenfunctions of the Laplace operator by means of discontinuous Galerkin (DG) methods. It results that several DG methods actually provide a spectrally correct approximation of the Laplace operator. We present here the convergence theory, which applies to a wide class of DG methods, as well as numerical tests demonstrating the t...

We build a bridge between the hybrid high-order (HHO) and the hybridizable discontinuous Galerkin (HDG) methods in the setting of a model diffusion problem. First, we briefly recall the construction of HHO methods and derive some new variants. Then, by casting the HHO method in mixed form, we identify the numerical flux so that the HHO method can be compared to HDG methods. In turn, the incorpo...

We propose a discontinuous finite element method for small strain elasticity allowing for cohesive zone modeling. The method yields a seamless transition between the discontinuous Galerkin method and classical cohesive zone modeling. Some relevant numerical examples are presented.

Basic iterative domain decomposition methods (DDM) can only transmit information between direct neighbors. Such methods never converge in less iterations than the diameter of the connectivity graph between subdomains. Convergence rates are dependent on the number of subdomains, and thus algorithms are not scalable. The use of a coarse space [16] is the only way to provide information from dista...