DOLFIN User Manual - FEniCS Project
DOLFIN User Manual - FEniCS Project DOLFIN User Manual - FEniCS Project
DOLFIN User ManualHoffman, Jansson, Logg, Wellsfaces by identifying an edge on a face with the opposite vertex on the face:f 0 : (e 5 , e 0 , e 4 ),f 1 : (e 3 , e 1 , e 5 ),f 2 : (e 2 , e 3 , e 4 ),f 3 : (e 0 , e 1 , e 2 ).(A.6)Note that the ordering of edges on f 3 is the same as the ordering of edgeson the reference triangle. Also note that the internal ordering of verticeson edges does not always follow the orientation of the face (which is notpossible).A.3 Ordering of degrees of freedomThe local and global orderings of degrees of freedom or nodes are obtainedby associating each node with a mesh entity, locally and globally.A.3.1Mesh entitiesWe distinguish between mesh entities of different topological dimensions:vertices topological dimension 0edges topological dimension 1faces topological dimension 2cells topological dimension 2 or 3A cell can be either a triangle or a tetrahedron depending on the type ofmesh. For a mesh consisting of triangles, the mesh entities involved arevertices, edges and cells, and for a mesh consisting of tetrahedrons, the meshentities involved are vertices, edges, faces and cells.90
DOLFIN User ManualHoffman, Jansson, Logg, Wellsx 2v 3 v 0 = (0, 0, 0)v 1 = (1, 0, 0)v 2 = (0, 1, 0)v 3 = (0, 0, 1)PSfrag replacementsv 0 v 1 v 2x 0x 1Figure A.3: Physical coordinates of the reference tetrahedron.91
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<strong>DOLFIN</strong> <strong>User</strong> <strong>Manual</strong>Hoffman, Jansson, Logg, Wellsx 2v 3 v 0 = (0, 0, 0)v 1 = (1, 0, 0)v 2 = (0, 1, 0)v 3 = (0, 0, 1)PSfrag replacementsv 0 v 1 v 2x 0x 1Figure A.3: Physical coordinates of the reference tetrahedron.91
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