A nonconforming method for a generalized Darcy-Forchheimer model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918464460947456 |
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| author | Botti, Michele Mascotto, Lorenzo Mosconi, Marialetizia |
| author_facet | Botti, Michele Mascotto, Lorenzo Mosconi, Marialetizia |
| contents | We analyze a dual mixed nonconforming discretization of a generalized Darcy-Forchheimer model. Compared to the analogous scheme proposed by Girault and Wheeler, we consider general, i.e., nonquadratic, Forchheimer nonlinearities; we admit mixed, inhomogeneous boundary conditions; we allow for more general, i.e., with lower Lebesgue regularity, permeability tensors; we construct general-order schemes; we prove convergence to the exact solution under low regularity assumptions, based on novel Sobolev-trace inequalities for broken spaces; we derive error estimates of general-order assuming extra regularity of the exact solution and data; we present numerical results assessing the performance of the proposed schemes for different types of nonlinearity and nonlinear solvers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_21558 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A nonconforming method for a generalized Darcy-Forchheimer model Botti, Michele Mascotto, Lorenzo Mosconi, Marialetizia Numerical Analysis 76S05, 65N12, 65N30 We analyze a dual mixed nonconforming discretization of a generalized Darcy-Forchheimer model. Compared to the analogous scheme proposed by Girault and Wheeler, we consider general, i.e., nonquadratic, Forchheimer nonlinearities; we admit mixed, inhomogeneous boundary conditions; we allow for more general, i.e., with lower Lebesgue regularity, permeability tensors; we construct general-order schemes; we prove convergence to the exact solution under low regularity assumptions, based on novel Sobolev-trace inequalities for broken spaces; we derive error estimates of general-order assuming extra regularity of the exact solution and data; we present numerical results assessing the performance of the proposed schemes for different types of nonlinearity and nonlinear solvers. |
| title | A nonconforming method for a generalized Darcy-Forchheimer model |
| topic | Numerical Analysis 76S05, 65N12, 65N30 |
| url | https://arxiv.org/abs/2604.21558 |