We prove in an abstract setting that standard (continuous) Galerkin finite element approximations are the limit of interior penalty discontinuous Galerkin approximations as the penalty parameter tends to infinity. We apply this result to equations of non-negative characteristic form and the non-linear, time dependent system of incompressible miscible displacement. Moreover, we investigate varyi...

The phase behavior of confined nematogens is studied using the Lebwohl-Lasher model. For three-dimensional systems the model is known to exhibit a discontinuous nematic-isotropic phase transition, whereas the corresponding two-dimensional systems apparently show a continuous Berezinskii-Kosterlitz-Thouless-like transition. In this paper, we study the phase transitions of the Lebwohl-Lasher mode...

A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations. This method, called WG-MFEM, is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary shape of polygons/polyhedra. The WG-MFEM is capable of providing very accurate numerical approximations for b...

Chaotic chattering behaviors of DC-DC converters are caused by the nonlinearity of the switching operation which is an essential characteristics of the power electronics circuits. In this paper the bifurcation and the appearance of the chaotic chattering in the discontinuous current conduction mode of a DC-DC buck converter are discussed experimentally. Moreover, a method for controlling chaoti...

The purpose of this paper is to study the discontinuous solutions to a shallow water wave equation with relaxation. The typical initial value problem of discontinuous solutions is the Riemann problem. Unlike the homogeneous hyperbolic conservation laws, due to the inhomogeneity of the system studied here, the solutions of the Riemann problem do not have a self-similar structure anymore. This pr...

In this paper we will extend the input-to-state stability (ISS) framework introduced by Sontag to continuous-time discontinuous dynamical systems adopting Filippov’s solution concept and using non-smooth ISS Lyapunov functions. The main motivation for investigating non-smooth ISS Lyapunov functions is the recent focus on “multiple Lyapunov functions” for which feasible computational schemes are...

In the current study, behavior of crank-slider mechanism with single and multiple clearance joints are analyzed. Using Lankarani-Nikravesh theory for estimating discontinuous contact forces in clearance joints, relevant systems have been mathematically modeled. Through numerical simulations, perturbations in response of mechanisms with clearance joints have been analyzed. Effects of increasing ...

In this paper we compute the maximum number of limit cycles of some classes of planar discontinuous piecewise linear differential systems defined in two half–planes separated by a straight line Σ. Here we only consider non–sliding limit cycles, i.e. the limit cycle does not contain any sliding segment. Among all the cases that we study, in particular, we prove that this maximum number of limit ...

In this paper the chaos persistence in a class of discontinuous dynamical systems of fractionalorder is analyzed. To that end, the Initial Value Problem is first transformed, by using the Filippov regularization [1], into a set-valued problem of fractional-order, then by Cellina’s approximate selection theorem [2, 3], the problem is approximated into a single-valued fractional-order problem, wh...

We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and control constraints. The optimal controller is allowed to be discontinuous including bang-bang control. Although the nonlinear system is assumed to be feedback linearizable, in general, the optimal control does not linearize the dynamics. The continuous optimal control problem is discretized usin...