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

This paper introduces a numerical scheme for the time-harmonic Maxwell equations by
using weak Galerkin (WG) finite element methods. The WG finite element method is based …

In this popular text for an Numerical Analysis course, the authors introduce several major
methods of solving various partial differential equations (PDEs) including elliptic, parabolic …

We present a discontinuous Galerkin surface integral equation method, herein referred to as
IEDG, for time harmonic electromagnetic wave scattering from nonpenetrable targets. The …

In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method
for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high …

In this paper, we develop the a posteriori error estimation of hp-version interior penalty
discontinuous Galerkin discretizations of elliptic boundary-value problems. Computable …

In this paper, we present a non-dissipative spatial high-order discontinuous Galerkin method
to solve the Maxwell equations in the time domain. The non-intuitive choice of the space of …

We develop the symmetric interior penalty discontinuous Galerkin (DG) method for the time-
dependent Maxwell equations in second-order form. We derive optimal a priori error …

We propose certified reduced basis methods for the efficient and reliable evaluation of a
general output that is implicitly connected to a given parameterized input through the …

A virtual element method (VEM) with the first-order optimal convergence order is developed
for solving two-dimensional Maxwell interface problems on a special class of polygonal …