Frequency-explicit approximability estimates for time-harmonic Maxwell’s equations

Gradient Estimates for Weak Solutions of A-Harmonic Equations

Frequency Explicit Regularity Estimates for the Electric Field Integral Operator

In this paper, we derive regularity estimates for the electric field integral operator which arises when formulating the time-harmonic Maxwell problem as a boundary integral equation. More precisely, we show that the regularity constants can be bounded polynomially in terms of the frequency, where the degree of the polynomial depends on the regularity order and is given explicitly. The paper co...

Abstract nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell's equations

nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell’s equations Alexandre Ern, Jean-Luc Guermond To cite this version: Alexandre Ern, Jean-Luc Guermond. Abstract nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell’s equations. 2017. HAL Id: hal-01563594...

A non-overlapping domain decomposition for low-frequency time-harmonic Maxwell's equations in unbounded domains

In this paper, we are concerned with a non-overlapping domain decomposition method for solving the low-frequency time-harmonic Maxwell’s equations in unbounded domains. This method can be viewed as a coupling of the finite element and the boundary element in unbounded domains, which are decomposed into two sub-domains with a spherical artificial boundary. We first introduce a discretization for...

Complete low frequency asymptotics for time-harmonic generalized Maxwell equations in nonsmooth exterior domains

We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in a nonsmooth exterior domain Ω ⊂ RN , N ≥ 3 , with nonsmooth inhomogeneous, anisotropic coefficients converging near infinity with a rate r−τ , τ > 1 , towards the identity. By means of the limiting absorption principle a Fredholm alternative holds true and the eigensolutions decay polynomially...