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A reimplementation of the Springer book: https://github.com/hplgit/fenics-tutorial/, covering new topics as well as transitioning from dolfin to dolfinx

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## Summary This pull request introduces an initial **monolithic CR–P0 steady Navier–Stokes solver**. ### Current contents - `chapter2/monolithic_navierstokes_crp0.py` — runnable solver with: - Crouzeix–Raviart (CR) velocity and DG–0 pressure formulation...

Description This issue proposes replacing the current ns_code1.py example with a monolithic incompressible Navier–Stokes solver implemented using the Crouzeix–Raviart (CR) element for velocity and DG-0 for pressure (CR–P0 pair). The...

In the Navier-Stokes introductory page, an intermediate step is described [here](https://jsdokken.com/dolfinx-tutorial/chapter2/navierstokes.html#equation-ipcs-one). By the definition of $u^{n+\frac12} = \frac12 (u^{n}+u^{n+1})$, the equation depends on $u^\ast$ as well as $u^{n+1}$. In the...

**Direct solver** PETSc does magic after the fact with nullspace information, which is "correct", but mumps might fail if icntl_24:1 and inctl_25: 0 is not set for more complex spaces....

Ref: https://fenicsproject.discourse.group/t/mixed-dimensional-diffusion-problem/18217/10?u=dokken ```python # # Ilustration of varying boundary conditions through physical parameters # Author: Jørgen S. Dokken # SPDX-License-Identifier: MIT from mpi4py import MPI import dolfinx.fem.petsc import ufl import...

For a particular study case of a slightly compressible hyperelastic disk subjected to uniform radial traction, using the hyperplasticity code with the Neo-Hookean model we encountered some instability phenomena. After...

enhancement

Derive a priori solution of the problem from known strain potential

Geometry, material properties, the governing equation, and the boundary condition. Most of it is generally very clear for someone in the computational mechanics. It took me some time to understand...