In the special case of the Laplace operator the vector
has the following form
![]() |
(3.60) |
For a grid with a regular distance
between neighboring vertices, the geometrical coefficient matrix
yields for five and nine neighboring points:
After eliminating derivatives which do not appear in the series expansion of the single points, the matrices can be re-written. The derivative vector
is written as:
![]() |
(3.61) |
The vector
is reduced to the following form:
![]() |
(3.62) |
Inserting into the formula (3.58) yields the well known expressions. The function
can be written as
For nine points the following formula is obtained:
Michael 2008-01-16