We present a compact discontinuous Galerkin (CDG) method for an elliptic model problem. The problem is first cast as a system of first order equations by introducing the gradient of the primal unknown, or flux, as an additional variable. A standard discontinuous Galerkin (DG) method is then applied to the resulting system of equations. The numerical interelement fluxes are such that the equatio...

in this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. a numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. truncation errors are derived for both continuous and discontinuous problems. parameter uni...

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 this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier–Stokes equations. For the discretization of the leading order terms, we propose employing the generalization of the symmetric version of the interior penalty method, originally developed for the numerical approximation of linear self-adjoint sec...

In this paper, feedback stabilization problem of nonholonomic chained system is studied. A new continuous and time-varying design approach is proposed and it is a pure state feedback control. By injecting an exponential decaying disturbance scaled by the norm of the states, u1 drives the initial states away from the singular manifold {x|x1 = 0, ‖x‖ 6= 0} that causes singularity. In addition to ...

When simulating hybrid discrete-continuous dynamical systems a key problem is the discontinuous model behavior. The state derivatives may change in a discontinuous way depending on the discrete state of the model. Conventional simulation algorithms are not suitable to integrate hybrid system models with high accuracy and reasonable computational e ort. In this paper we present results obtained ...

We present a model-based monitoring method for dynamic systems that exhibit both discrete and continuous behaviors. MIMIC [Dvorak and Kuipers, 1991] uses qualitative and semiquantitative models to monitor dynamic systems even with incomplete knowledge. Recent advances have improved the quality of semi-quantitative behavior predictions, used observations to refine static envelopes around monoton...

This paper is concerned with a weakly coupled system of quasilinear parabolic equations where the coefficients are allowed to be discontinuous and the reaction functions may depend on continuous delays. By the method of upper and lower solutions and the associated monotone iterations and by difference ratios method and various estimates, we obtained the existence and uniqueness of the global pi...

The discontinuous Galerkin time-domain method (DGTD) is an emerging technique for the numerical simulation of time-dependent electromagnetic phenomena. For many applications it is necessary to model the infinite space which surrounds scatterers and sources. As a result, absorbing boundaries which mimic its properties play a key role in making DGTD a versatile tool for various kinds of systems. ...

We consider the system of equations governing an incompressible immiscible two-phase flow within an heterogeneous porous medium made of two different rock types. Since the capillary pressure function depends on the rock type, the capillary pressure field might be discontinuous at the interface between the rocks. We introduce multivalued phase pressures to give a sense to the transmission condit...