Equivalence of mixed and nonconforming methods on general polytopal partitions. Part I: Multiscale and projection methods
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| Formato: | Preprint |
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2026
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| _version_ | 1866917277709893632 |
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| author | Lemaire, Simon |
| author_facet | Lemaire, Simon |
| contents | We study equivalence, in the context of a variable diffusion problem, between (conforming) mixed methods and (primal) nonconforming methods defined on potentially general polytopal partitions. In this first paper of a series of two, we focus on multiscale and projection methods. For multiscale methods, we establish the first-level equivalence between four different (oversampling-free) approaches, thereby broadening the results of [Chaumont-Frelet, Ern, Lemaire, Valentin; M2AN, 2022]. For projection methods, in turn, we provide a simple criterion (to be checked in practice) for primal/mixed well-posedness and equivalence to hold true. In the process, we also shed a new light on some self-stabilized hybrid methods. Part II of this work will address (general) polytopal element methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15193 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivalence of mixed and nonconforming methods on general polytopal partitions. Part I: Multiscale and projection methods Lemaire, Simon Numerical Analysis 65N30, 65N08, 76R50 We study equivalence, in the context of a variable diffusion problem, between (conforming) mixed methods and (primal) nonconforming methods defined on potentially general polytopal partitions. In this first paper of a series of two, we focus on multiscale and projection methods. For multiscale methods, we establish the first-level equivalence between four different (oversampling-free) approaches, thereby broadening the results of [Chaumont-Frelet, Ern, Lemaire, Valentin; M2AN, 2022]. For projection methods, in turn, we provide a simple criterion (to be checked in practice) for primal/mixed well-posedness and equivalence to hold true. In the process, we also shed a new light on some self-stabilized hybrid methods. Part II of this work will address (general) polytopal element methods. |
| title | Equivalence of mixed and nonconforming methods on general polytopal partitions. Part I: Multiscale and projection methods |
| topic | Numerical Analysis 65N30, 65N08, 76R50 |
| url | https://arxiv.org/abs/2602.15193 |