It has been shown that the barycentric coordinates transform each triangular and tetrahedron element in the unit triangle and tetrahedron, respectively. (Refer to Fig. <4.3> and Fig. <4.8>.) This is used for the analytical calculation of the arising integral terms, when the element matrices are assembled.
The two-dimensional domain
is transformed to
by
the expressions
![]() |
(A.1) |
![]() |
![]() |
(A.2) |
The area
of the
-th element
is approximately related by
the vector product
![]() |
(A.3) |
and
![]() |
(A.4) |
where
![]() |
(A.5) |
For sufficiently small
and
the face
is expressed as
![]() |
(A.6) |
with
Analogously the transformation for the three-dimensional case can be expressed by:
with