Solving the (Navier-)Stokes equations with space and time adaptivity using deal.II
arXiv:2603.29621
Abstract
In this article, we solve the Stokes and Navier-Stokes equations with the dealII 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 dealII.
13 pages, 6 figures, 3 tables, submitted for proceedings of ENUMATH 2025