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Here the chosen enrichment is the Heavyside function
with:
and
. The formulation using
the time stepping scheme (20) is:
in assuming that:
where
is the Dirac function.
First, the approximation of was
.It gives the results shown on Fig.16.
Figure 16:
The results for the XFEM, first shot.
|
But a better approximation of between the time steps and was
. This approximation permits to the
algorithm to give the exact solution as shown on Fig. 17.
Figure 17:
The X-FEM gives the exact solution.
|
Next: APPLICATION TO PROBLEMS WITH
Up: Second Problem: the shock
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Renaud Merle
2000-08-26