In this paper, we develop and analyze the Runge-Kutta discontinuous Galerkin (RKDG) method to solve weakly coupled hyperbolic multi-domain problems. Such problems involve transfer type boundary conditions with discontinuous fluxes between different domains, calling for special techniques to prove stability of the RKDG methods. We prove both stability and error estimates for our RKDG methods on ...

Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010; Naghshtabrizi, Hespanha, & Teel, 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger’s inequality. These fun...

In Computable Analysis each computable function is continuous and computably invariant , i.e. it maps computable points to computable points. On the other hand, discontinuity is a suucient condition for non-computability, but a discontinuous function might still be computably invariant. We investigate algebraic conditions which guarantee that a discon-tinuous function is suuciently discontinuou...

We numerically solve parabolic problems in , , where is a bounded interval and is a strongly elliptic integrodifferential operator of order ! #" %$'& . A discontinuous Galerkin (dG) discretization in time and a wavelet discretization in space are used. The densely populated matrices in the corresponding linear systems of equations are replaced by sparse ones using appropriate wavelet compressio...

Reduced switching loss favours Pulse Skipping Modulation mode of switching dc-to-dc converters at light loads. Under certain conditions the converter operates in discontinuous conduction mode (DCM). Inductor current starts from zero in each switching cycle as the switching frequency is constant and not adequately high. A DC-to-DC buck converter is modelled and simulated in this paper under DCM....

This paper presents discontinuous Legendre wavelet Galerkin (DLWG) approach for solving onedimensional advection-diffusion equation (ADE). Variational formulation of this type equation and corresponding numerical fluxes are devised by utilizing the advantages of both the Legendre wavelet bases and discontinuous Galerkin (DG) method. The distinctive features of the proposed method are its simple...

This paper proves the equilibrium existence for abstract economies with non-compact infinitedimensional strategy spaces, infinitely many agents, and discontinuous payolT (utility) functions by using the quasi-variational inequality approach. The motivations come from economic applications showing that payoff functions are discontinuous in many cases and the set of feasible allocations generally...

In this paper, we consider the div-curl problem posed on nonconvex polyhedral domains. We propose a least-squares method based on discontinuous elements with normal and tangential continuity across interior faces, as well as boundary conditions, weakly enforced through a properly designed least-squares functional. Discontinuous elements make it possible to take advantage of regularity of given ...

A discretization scheme applicable to the direct approximation of the velocity variable for either a rst-order system or second-order elliptic equation is proposed in this paper. The scheme is motivated by mixed nite element methods and extends the cell-centered nite diierence and the nite volume element methods to problems with discontinuous coeecients and various boundary conditions. Error es...

We present results of a discontinuous Galerkin scheme applied to deterministic computations of the transients for the Boltzmann-Poisson system describing electron transport in semiconductor devices. The collisional term models optical-phonon interactions which become dominant under strong energetic conditions corresponding to nano-scale active regions under applied bias. The proposed numerical ...