Many more topics could be treated in a FEniCS tutorial, e.g., how to solve systems of PDEs, how to work with mixed finite element methods, how to create more complicated meshes and mark boundaries, and how to create more advanced visualizations. However, to limit the size of this tutorial, the examples end here. There are, fortunately, a rich set of FEniCS demos. The FEniCS documentation explains a collection of PDE solvers in detail: the Poisson equation, the mixed formulation for the Poission equation, the Biharmonic equation, the equations of hyperelasticity, the Cahn-Hilliard equation, and the incompressible Navier-Stokes equations. Both Python and C++ versions of these solvers are explained. An eigenvalue solver is also documented. In the dolfin/demo directory of the DOLFIN source code tree you can find programs for these and many other examples, including the advection-diffusion equation, the equations of elastodynamics, a reaction-diffusion equation, various finite element methods for the Stokes problem, discontinuous Galerkin methods for the Poisson and advection-diffusion equations, and an eigenvalue problem arising from electromagnetic waveguide problem with Nedelec elements. There are also numerous demos on how to apply various functionality in FEniCS, e.g., mesh refinement and error control, moving meshes (for ALE methods), computing functionals over subsets of the mesh (such as lift and drag on bodies in flow), and creating separate subdomain meshes from a parent mesh.
The project cbc.solve (https://launchpad.net/cbc.solve) offers more complete PDE solvers for the Navier-Stokes equations, the equations of hyperelasticity, fluid-structure interaction, viscous mantle flow, and the bidomain model of electrophysiology. Most of these solvers are described in the “FEniCS book” [FEniCS] (https://launchpad.net/fenics-book). Another project, cbc.rans (https://launchpad.net/cbc.rans), offers an environment for very flexible and easy implementation of Navier-Stokes solvers and turbulence [Mortensen2011] [Mortensen2011b]. For example, cbc.rans contains an elliptic relaxation model for turbulent flow involving 18 nonlinear PDEs. FEniCS proved to be an ideal environment for implementing such complicated PDE models. The easy construction of systems of nonlinear PDEs in cbc.rans has been further generalized to simplify the implementation of large systems of nonlinear PDEs in general. The functionality is found in the cbc.pdesys package (https://launchpad.net/cbcpdesys).