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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2510.25298 |
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| _version_ | 1866915585338638336 |
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| author | Xu, Liangkun Wang, Shixi Bi, Hai |
| author_facet | Xu, Liangkun Wang, Shixi Bi, Hai |
| contents | In this paper, we discuss a virtual element approximation for the modified transmission eigenvalue problem in inverse scattering for natural materials. In this case, due to the positive artificial diffusivity parameter in the considered problem, the sesquilinear form at the left end of the variational form is not coercive. We first demonstrate the well-posedness of the discrete source problem using the $\mathds{T}$-coercivity property, then provide the a priori error estimates for the approximate eigenspaces and eigenvalues, and finally reports several numerical examples. The numerical experiments show that the proposed method is effective |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25298 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A virtual element approximation for the modified transmission eigenvalues for natural materials Xu, Liangkun Wang, Shixi Bi, Hai Numerical Analysis In this paper, we discuss a virtual element approximation for the modified transmission eigenvalue problem in inverse scattering for natural materials. In this case, due to the positive artificial diffusivity parameter in the considered problem, the sesquilinear form at the left end of the variational form is not coercive. We first demonstrate the well-posedness of the discrete source problem using the $\mathds{T}$-coercivity property, then provide the a priori error estimates for the approximate eigenspaces and eigenvalues, and finally reports several numerical examples. The numerical experiments show that the proposed method is effective |
| title | A virtual element approximation for the modified transmission eigenvalues for natural materials |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.25298 |