Preasymptotic error estimates of higher-order EEM for the time-harmonic Maxwell equations with large wave number
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911281807622144 |
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| author | Lu, Shuaishuai Wu, Haijun |
| author_facet | Lu, Shuaishuai Wu, Haijun |
| contents | The time-harmonic Maxwell equations with impedance boundary condition and large wave number are discretized using the second-type Nédélec's edge element method (EEM). Preasymptotic error bounds are derived, showing that, under the mesh condition $κ^{2p+1}h^{2p}$ being sufficiently small, the error of the EEM of order $p$ in the energy norm is bounded by $\mathcal{O}\big(κ^{p}h^p + κ^{2p+1}h^{2p}\big)$, while the error in the $κ$-scaled $\boldsymbol{L}^2$ norm is bounded by $\mathcal{O}\big((κh)^{p+1} + κ^{2p+1} h^{2p}\big)$. Here, $κ$ is the wave number and $h$ is the mesh size. Numerical tests are provided to illustrate our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19481 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Preasymptotic error estimates of higher-order EEM for the time-harmonic Maxwell equations with large wave number Lu, Shuaishuai Wu, Haijun Numerical Analysis The time-harmonic Maxwell equations with impedance boundary condition and large wave number are discretized using the second-type Nédélec's edge element method (EEM). Preasymptotic error bounds are derived, showing that, under the mesh condition $κ^{2p+1}h^{2p}$ being sufficiently small, the error of the EEM of order $p$ in the energy norm is bounded by $\mathcal{O}\big(κ^{p}h^p + κ^{2p+1}h^{2p}\big)$, while the error in the $κ$-scaled $\boldsymbol{L}^2$ norm is bounded by $\mathcal{O}\big((κh)^{p+1} + κ^{2p+1} h^{2p}\big)$. Here, $κ$ is the wave number and $h$ is the mesh size. Numerical tests are provided to illustrate our theoretical results. |
| title | Preasymptotic error estimates of higher-order EEM for the time-harmonic Maxwell equations with large wave number |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.19481 |