Considering only the scalar functions
the Neumann boundary term (5.31)
is written
![]() |
(C.27) |
The matrix
can be constructed by the element matrix
with entries
![]() |
(C.28) |
is the element face lying on the Neumann boundary
and
is the corresponding normal vector pointing outwards.
is assumed as constant
scalar in each element. Again the element matrix is constructed for the four triangular
faces (from
to
) of the tetrahedron.
For
:
Since
is 0
on
![]() |
(C.29) |
For the second row the following expression is obtained
![]() |
(C.30) |
Analogously the entries of the next rows are calculated
![]() |
(C.31) |
The non-zero entries do not depend on the row index but on the face and column index. Consequently the non-zero rows are identical.
Similarly it is proceeded for the remaining element faces.
For
:
![]() |
(C.32) |
For
:
![]() |
(C.33) |
For
:
![]() |
(C.34) |