相关论文: Energy norm error estimates and convergence analys…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…
One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…
In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…
It is pointed out that the usual derivation of the well-known Maxwell electromagnetic equations holds only for a medium at rest. A way in which the equations may be modified for the case when the mean flow of the medium is steady and…
The differential form of the Maxwell's equations was first derived based on an assumption that the media are stationary, which is the foundation for describing the electro-magnetic coupling behavior of a system. For a general case in which…
This paper presents a stable finite element approximation for the acoustic wave equation on second-order form, with perfectly matched layers (PML) at the boundaries. Energy estimates are derived for varying PML damping for both the discrete…
This note offers a conceptually straightforward and efficient way to formulate and solve problems in the electromagnetics of moving media based on a representation of Maxwell's equations in terms of differential forms on spacetime together…
We consider the static Maxwell system with an axially symmetric dielectric permittivity and construct complete systems of its solutions which can be used for analytic and numerical solution of corresponding boundary value problems.
We analyze the conforming approximation of the time-harmonic Maxwell's equations using N\'ed\'elec (edge) finite elements. We prove that the approximation is asymptotically optimal, i.e., the approximation error in the energy norm is…
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…
In a bounded domain $\mathcal{O}\subset\mathbb{R}^3$ of class $C^{1,1}$, we consider a stationary Maxwell system with the perfect conductivity boundary conditions. It is assumed that the dielectric permittivity and the magnetic permeability…
Stability and convergence analysis for the domain decomposition finite element/finite difference (FE/FD) method is presented. The analysis is designed for semi-discrete finite element scheme for the time-dependent Maxwell's equations. The…
We are concerned with increasing stability in the inverse source problems for the time-dependent Maxwell equations in R^3 , where the source term is compactly supported in both time and spatial variables. By using the Fourier transform,…
Temporal metamaterials are artificially manufactured materials with time-dependent material properties that exhibit interesting phenomena when waves propagate through them. The propagation of electromagnetic waves in such time-varying…
It is shown in linear approximation that in the case of one-dimensional problem of transverse electron waves in a half-infinite slab of homogeneous Maxwellian collisionless plasma with the given boundary field frequency two wave branches of…
Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…
The time-harmonic Maxwell equations at high wavenumber k in domains with an analytic boundary and impedance boundary conditions are considered. A wavenumber-explicit stability and regularity theory is developed that decomposes the solution…
We present a stability and convergence analysis of the space-time continuous finite element method for the Hamiltonian formulation of the wave equation. More precisely, we prove a continuous dependence of the discrete solution on the data…
We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…