In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing parameters are large enough to stabilize the method. A central idea in the analysis is to construct an auxiliary solution from the discontinuous Galerkin solution by ...

H istorically, ecology has focused on continuous distributions and smooth transitions. Only recently have discontinuities and thresholds become an explicit focus in some areas of ecology, especially in the realm of complex systems. The study of animal body mass distributions has been recognized for its potential to provide insight into the underlying processes shaping animal communities. Hutchi...

We prove stability and derive error estimates for the recently introduced central discontinuous Galerkin method, in the context of linear hyperbolic equations with possibly discontinuous solutions. A comparison between the central discontinuous Galerkin method and the regular discontinuous Galerkin method in this context is also made. Numerical experiments are provided to validate the quantitat...

Three discontinuous operating modes of PWM converters are considered in this paper-the discontinuous inductor current mode (DICM), the discontinuous capacitor voltage mode (DCVM) and a previously unidentified mode named discontinuous quasi-resonant mode (DQRM). DC and smallsignal ac analyses are applicable to all basic PWM converter topologies. Any particular topology is taken into account via ...

Proliferation of degrees-of-freedom has plagued discontinuous Galerkin methodology from its inception over 30 years ago. This paper develops a new computational formulation that combines the advantages of discontinuous Galerkin methods with the data structure of their continuous Galerkin counterparts. The new method uses local, element-wise problems to project a continuous finite element space ...

In the absolutely continuous case, order statistics, record values and several other models of ordered random variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither re...