Preasymptotic error estimates of EEM and CIP-EEM for the time-harmonic Maxwell equations with large wave number
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929415125991424 |
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| author | Lu, Shuaishuai Wu, Haijun |
| author_facet | Lu, Shuaishuai Wu, Haijun |
| contents | 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 $κ^3 h^2$ is sufficiently small, the errors of the solutions to both methods are bounded by $\mathcal{O} (κh + κ^3 h^2 )$ in the energy norm and $\mathcal{O} (κh^2 + κ^2 h^2 )$ in the $\boldsymbol{L}^2$ norm, where $κ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Preasymptotic error estimates of EEM and CIP-EEM for the time-harmonic Maxwell equations with large wave number Lu, Shuaishuai Wu, Haijun Numerical Analysis 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 $κ^3 h^2$ is sufficiently small, the errors of the solutions to both methods are bounded by $\mathcal{O} (κh + κ^3 h^2 )$ in the energy norm and $\mathcal{O} (κh^2 + κ^2 h^2 )$ in the $\boldsymbol{L}^2$ norm, where $κ$ 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. |
| title | Preasymptotic error estimates of EEM and CIP-EEM for the time-harmonic Maxwell equations with large wave number |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2407.06784 |