Appendix

Mesh import

GMSH + dolfin-convert [http://geuz.org/gmsh]

1. Use GMSH to create your domain; mark boundaries either by gmsh gui or by preparing gmsh script (see bench.geo example).
2. Generate the mesh by gmsh -2 yourdomain.geo or gmsh -3 yourdomain.geo for 3D mesh
3. Run: dolfin-convert yourdomain.msh yourdomain.xml
4. Then in the FEniCS script you can read the XML mesh:

mesh = Mesh("yourdomain.xml")
cell_function = MeshFunction("size_t", mesh, "yourdomain_physical_region.xml")
facet_function = MeshFunction("size_t", mesh, "yourdomain_facet_region.xml")

Local mesh refinement

markers = CellFunction("bool", mesh)
markers.set_all(False)
for c in cells(mesh):
    # Mark cells with facet midpoints near y == 1.0
    for f in facets(c):
        if near(f.midpoint()[1], 1.0):
            markers[c] = True
mesh = refine(mesh, markers, redistribute=False)

This will create new mesh object. For adaptivity see adaptive Poisson demo and adapt method reference.

Applications built on top of FEniCS

See Applications page of FEniCS project.

What every computer scientist should know about floating-point arithmetic

(Goldberg, 1991) pdf

Periodic table of finite elements

femtable.org