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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.29621 |
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| _version_ | 1866911557613518848 |
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| author | Munch, Peter Fehling, Marc Kronbichler, Martin Margenberg, Nils Saavedra, Laura Prieto |
| author_facet | Munch, Peter Fehling, Marc Kronbichler, Martin Margenberg, Nils Saavedra, Laura Prieto |
| contents | In this article, we solve the Stokes and Navier-Stokes equations with the deal$.$II finite-element library. In particular, we use its multigrid, adaptive-mesh, and matrix-free infrastructures to design efficient linear and nonlinear iterative solvers, respectively. We solve the stationary Stokes equations on hp-adaptive meshes with a hp-multigrid approach, the transient Stokes equations with space-time finite elements and space-time multigrid, and, finally, the stabilized incompressible Navier-Stokes equations on locally refined meshes with a monolithic multigrid solver. The selected examples underline the flexibility and modularity of the multigrid infrastructure of deal$.$II. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29621 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solving the (Navier-)Stokes equations with space and time adaptivity using deal.II Munch, Peter Fehling, Marc Kronbichler, Martin Margenberg, Nils Saavedra, Laura Prieto Numerical Analysis Computational Physics In this article, we solve the Stokes and Navier-Stokes equations with the deal$.$II finite-element library. In particular, we use its multigrid, adaptive-mesh, and matrix-free infrastructures to design efficient linear and nonlinear iterative solvers, respectively. We solve the stationary Stokes equations on hp-adaptive meshes with a hp-multigrid approach, the transient Stokes equations with space-time finite elements and space-time multigrid, and, finally, the stabilized incompressible Navier-Stokes equations on locally refined meshes with a monolithic multigrid solver. The selected examples underline the flexibility and modularity of the multigrid infrastructure of deal$.$II. |
| title | Solving the (Navier-)Stokes equations with space and time adaptivity using deal.II |
| topic | Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2603.29621 |