Glossary

Convex

See element

Cubature method

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 discribed.

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.