We study the dynamical behavior of the discontinuous Galerkin finite element method for initial value problems in ordinary differential equations. We make two different assumptions which guarantee that the continuous problem defines a dissipative dynamical system. We show that, under certain conditions, the discontinuous Galerkin approximation also defines a dissipative dynamical system and we ...

A functional differential inclusion-based approach to L2-gain analysis and feedback control problems is presented for a class of discontinuous time-delay systems. Motivated by Filippov solution in the differential equations with discontinuous right-hand side, definition of the discontinuous time-delay systems forced by external signals is introduced, and a description of L2-gain property in the...

This paper presents various patterns and computer art from three extensions to common fractal methods: use of discontinuous functions (such as boolean functions, and the conditional function), plots of root-finding methods other than Halley’s and Newton’s methods (such as Aitken’s and Muller’s methods), and fractals produced using arithmetic in q-systems other than the complex number system. St...

The drive-response synchronization of delayed neural networks with discontinuous activation functions is investigated via adaptive control.The synchronization of this paper means that the synchronization error approaches to zero for almost all time as time goes to infinity. The discontinuous activation functions are assumed to be monotone increasing which can be unbounded. Due to the mild condi...

This article introduces a novel transition system for discontinuous lexicalized constituent parsing called SR-GAP. It is an extension of the shift-reduce algorithm with an additional gap transition. Evaluation on two German treebanks shows that SR-GAP outperforms the previous best transitionbased discontinuous parser (Maier, 2015) by a large margin (it is notably twice as accurate on the predic...

in this paper, the linearly conforming enriched radial basis point interpolation method is implemented for the elasto-plastic analysis of discontinuous medium. the linear conformability of the method is satisfied by the application of stabilized nodal integration and the enrichment of radial basis functions is achieved by the addition of linear polynomial terms. to implement the method for the ...

A discontinuous Galerkin finite element method for an optimal control problem related to semilinear parabolic PDE’s is examined. The schemes under consideration are discontinuous in time but conforming in space. Convergence of discrete schemes of arbitrary order is proven. In addition, the convergence of discontinuous Galerkin approximations of the associated optimality system to the solutions ...

This paper considers discrete-time nonlinear, possibly discontinuous, systems in closed-loop with Model Predictive Controllers (MPC). The aim of the paper is to provide a priori sufficient conditions for asymptotic stability in the Lyapunov sense and robust stability, while allowing for both the system dynamics and the value function of the MPC cost to be discontinuous functions of the state. T...