A cubature method on an element consists in a set of nodes
(generally called gauss points) and corresponding loads which
define a approximated integration method. In GetFEM it is defined
on the reference elements.
Degree of freedom
The degrees of freedom for a finite element method is the coefficients
which multiply the shape functions in order to describe a
(scalar or vector) field. Generally, they are the unknowns of the
problem in general.
Element
An element is a small piece of a domain with a special shape (a segment,
a triangle, a quadrilateron, an tetrahedron, a hexahedron or a prism)
for dimensions less or equal to three. A mesh is the union of
non intersecting elements.
Finite element method (fem)
A finite element method is defined on a real element. It consist on a
certain number of degrees of freedom linked to the corresponding shape
functions and a manner to glue the degrees of freedom from a element
to a neighbour element.
Integration method
See cubature method.
Quadrature method
See cubature method.
Mesh
The mesh is composed of elements. in GetFEM, these elements are
often called convexes. A mesh can be composed of elements of different
dimensions (triangles, segments, quadrilaters, tetrahedra,
hexahedra …).
Mesh_Fem
The mesh_fem object is a mesh with a finite element method defined
on each element. This
represent a finite element space on which a unknown or a data on the
considered domain will be described.
Mesh_Im
The mesh_im object is a mesh with a cubature method defined on
each element. It is used in assembly procedures.
Reference element
A reference element or a convex of reference is a special element
on which the elementary computations (integrals) are performed.
For instance, the reference segment in GetFEM is the segment [0,1].
The reference triangle is the triangle (0,0), (0,1), (1,0). etc.
