A low-order locking-free multiscale finite element method for isotropic elasticity
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909149517840384 |
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| author | Gomes, Antônio Tadeu Azevedo Pereira, Weslley da Silva Valentin, Frédéric |
| author_facet | Gomes, Antônio Tadeu Azevedo Pereira, Weslley da Silva Valentin, Frédéric |
| contents | The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a family of low-order finite elements for the linear elasticity problem which are free from Poisson locking. The finite elements rely on face degrees of freedom associated with multiscale bases obtained from local Neumann problems with piecewise polynomial interpolations on faces. We establish sufficient refinement levels on the fine-scale mesh such that the MHM method is well-posed, optimally convergent under local regularity conditions, and locking-free. Two-dimensional numerical tests assess theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16890 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A low-order locking-free multiscale finite element method for isotropic elasticity Gomes, Antônio Tadeu Azevedo Pereira, Weslley da Silva Valentin, Frédéric Numerical Analysis 65N30, 65N12, 65N22 The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a family of low-order finite elements for the linear elasticity problem which are free from Poisson locking. The finite elements rely on face degrees of freedom associated with multiscale bases obtained from local Neumann problems with piecewise polynomial interpolations on faces. We establish sufficient refinement levels on the fine-scale mesh such that the MHM method is well-posed, optimally convergent under local regularity conditions, and locking-free. Two-dimensional numerical tests assess theoretical results. |
| title | A low-order locking-free multiscale finite element method for isotropic elasticity |
| topic | Numerical Analysis 65N30, 65N12, 65N22 |
| url | https://arxiv.org/abs/2403.16890 |