Wavenumber-explicit $hp$-FEM analysis for Maxwell's equations with transparent boundary conditions

Abstract

The time-harmonic Maxwell equations at high wavenumber $k$ are discretized by edge elements of degree $p$ on a mesh of width $h$. For the case of a ball and exact, transparent boundary conditions, we show quasi-optimality of the Galerkin method under the $k$-explicit scale resolution condition that a) $kh/p$ is sufficient small and b) $p/\log k$ is bounded from below.

References in corpus (4)

• On Bogovski\uı and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains
• On stability of discretizations of the Helmholtz equation (extended version)
• On commuting $p$-version projection-based interpolation on tetrahedra
• Wavenumber-explicit hp-FEM analysis for Maxwell's equations with impedance boundary conditions

Cited by in corpus (6)

• Frequency-explicit a posteriori error estimates for finite element discretizations of Maxwell's equations
• Frequency-explicit approximability estimates for time-harmonic Maxwell's equations
• Optimal convergence rates in $L^2$ for a first order system least squares finite element method. Part I: homogeneous boundary conditions
• Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations
• Numerical analysis of the high-frequency Helmholtz equation using semiclassical analysis
• Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides