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Main Authors: Munch, Peter, Fehling, Marc, Kronbichler, Martin, Margenberg, Nils, Saavedra, Laura Prieto
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.29621
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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