Preasymptotic Error Estimates of Linear EEM and CIP-EEM for the Time-Harmonic Maxwell Equations with Large Wave Number
Abstract
Abstract. Preasymptotic error estimates are derived for the second-type Nédélec linear edge element method and the linear [Formula: see text]-conforming interior penalty edge element method (CIP-EEM) for the time-harmonic Maxwell equations with large wave number. It is shown that under the mesh condition that [Formula: see text] is sufficiently small, the errors of the solutions to both methods are bounded by [Formula: see text] in the energy norm and [Formula: see text] in the [Formula: see text]-scaled [Formula: see text] norm, where [Formula: see text] is the wave number and [Formula: see text] is the mesh size. Numerical tests are provided to illustrate our theoretical results and the potential of CIP-EEM in significantly reducing the pollution effect.
Fields of Study & Subjects
Electromagnetic Simulation and Numerical Methods
Advanced Mathematical Physics Problems
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- SIAM Journal on Numerical Analysis
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 64
- Issue
- 2
- Pages
- 326–349
- Publication date
- 3 March 2026
- Language
- EN