The unknown field in the tetrahedral element (Fig. <4.7>) is approximated by the linear function
Analogously to the two-dimensional case the four coefficients
,
,
and
are obtained assuming that the field values
,
,
and
on the four vertexes of the tetrahedron are known.
The Jacoby determinant for the three-dimensional case is given by
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(4.64) |
where
is the volume of the tetrahedron. Equations (4.60) to
(4.63) define the auxiliary coefficients
,
,
and
(
), which are used to write (4.58) as
to introduce the element shape functions
.