This book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …

Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

The International Conference on Ad-Hoc Networks and Wireless (ADHOC-NOW) has
become a well-known venue for research dedicated to wireless sensor networks and mobile …

Finite difference operators approximating second derivatives with variable coefficients and
satisfying a summation-by-parts rule have been derived for the second-, fourth-and sixth …

Locally refined meshes impose severe stability constraints on explicit time-stepping methods
for the numerical simulation of time dependent wave phenomena. To overcome that stability …

In Grote et al.(SIAM J. Numer. Anal., 44: 2408–2431, 2006) a symmetric interior penalty
discontinuous Galerkin (DG) method was presented for the time-dependent wave equation …

In this paper, we develop a nodal discontinuous Galerkin method for solving the time-
dependent Maxwellʼs equations when metamaterials are involved. Both semi-and fully …

This paper adapts the weak Galerkin (WG) finite element scheme to Maxwell's equations in
the time domain. Developed by Wang and Ye in 2011, the WG scheme is a discontinuous …

Explicit local time-stepping methods are derived for time dependent Maxwell equations in
conducting and non-conducting media. By using smaller time steps precisely where smaller …

A stable and accurate boundary treatment is derived for the second-order wave equation.
The domain is discretized using narrow-diagonal summation by parts operators and the …