Preasymptotic error estimates of EEM and CIP-EEM for the time-harmonic Maxwell equations with large wave number

Shuaishuai Lu; Haijun Wu

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arXiv · 2407.06784

Preasymptotic error estimates of EEM and CIP-EEM for the time-harmonic Maxwell equations with large wave number

Shuaishuai Lu·Haijun Wu

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Abstract

Preasymptotic error estimates are derived for the linear edge element method (EEM) and the linear $\boldsymbol{H}(\boldsymbol{\mathrm{curl}})$-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 $\kappa^3 h^2$ is sufficiently small, the errors of the solutions to both methods are bounded by $\mathcal{O} (\kappa h + \kappa^3 h^2 )$ in the energy norm and $\mathcal{O} (\kappa h^2 + \kappa^2 h^2 )$ in the $\boldsymbol{L}^2$ norm, where $\kappa$ is the wave number and $h$ is the mesh size. Numerical tests are provided to verify our theoretical results and to illustrate the potential of CIP-EEM in significantly reducing the pollution effect.

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Shuaishuai Lu, Haijun Wu. 2024-07-09. Preasymptotic error estimates of EEM and CIP-EEM for the time-harmonic Maxwell equations with large wave number. https://arxiv.org/abs/2407.06784

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