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In order to get a more detailed impression of the quality of a solution,
one can show graphs of the function
in the following one-dimensional subsets of
. The following choices seem most relevant:
- Along fixed vertical cuts
to get an impression of the global behaviour.
- Along fixed horizontal cuts
to get an impression of the global behaviour.
- Along
-dependent radial cuts
to get an impression of the boundary layer behaviour.
- Along
-dependent horizontal cuts
to get an impression of the interior layer behaviour.
Figure 8:
The location of the cuts in the
-plane.
Horizontal cuts along
![$y=0,1-\varepsilon ^{1/2},1,1+\varepsilon ^{1/2}$](img7.png) ,
vertical cuts at ![$x=-1,0,1,2,4$](img53.png) and radial cuts at
![$r=1+\varepsilon ^k$](img54.png) ,
![$k= 1, 2/3, 1/3$](img55.png) .
|
As an example, in the Figures 9, 10 11 and 12
we show results for these cuts for the case
.
Figure 9:
The solution
along vertical cuts in the
-plane.
|
Figure 10:
The solution
along radial cuts in the
-plane.
|
Figure 11:
The solution
along horizontal cuts
in the
-plane.
|
Figure 12:
The solution
along horizontal cuts
in the
-plane.
|
Next: Function values at particular
Up: Representing numerical results
Previous: The global representation