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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.12609 |
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| _version_ | 1866916866052587520 |
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| author | Bressan, Andrea Mascotto, Lorenzo Mosconi, Marialetizia |
| author_facet | Bressan, Andrea Mascotto, Lorenzo Mosconi, Marialetizia |
| contents | We construct new Crouzeix-Raviart (CR) spaces of even degree $p$ that are spanned by basis functions mimicking those for the odd degree case. Compared to the standard CR gospel, the present construction allows for the use of nested bases of increasing degree and is particularly suited to design variable order CR methods. We analyze a nonconforming discretization of a two dimensional Poisson problem, which requires a DG-type stabilization; the employed stabilization parameter is considerably smaller than that needed in DG methods. Numerical results are presented, which exhibit the expected convergence rates for the $h$-, $p$-, and $hp$-versions of the scheme. We further investigate numerically the behaviour of new even degree CR-type discretizations of the Stokes' equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12609 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New Crouzeix-Raviart elements of even degree: theoretical aspects, numerical performance, and applications to the Stokes' equations Bressan, Andrea Mascotto, Lorenzo Mosconi, Marialetizia Numerical Analysis 65M12, 65M15 We construct new Crouzeix-Raviart (CR) spaces of even degree $p$ that are spanned by basis functions mimicking those for the odd degree case. Compared to the standard CR gospel, the present construction allows for the use of nested bases of increasing degree and is particularly suited to design variable order CR methods. We analyze a nonconforming discretization of a two dimensional Poisson problem, which requires a DG-type stabilization; the employed stabilization parameter is considerably smaller than that needed in DG methods. Numerical results are presented, which exhibit the expected convergence rates for the $h$-, $p$-, and $hp$-versions of the scheme. We further investigate numerically the behaviour of new even degree CR-type discretizations of the Stokes' equations. |
| title | New Crouzeix-Raviart elements of even degree: theoretical aspects, numerical performance, and applications to the Stokes' equations |
| topic | Numerical Analysis 65M12, 65M15 |
| url | https://arxiv.org/abs/2502.12609 |