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The X-FEM

Here the chosen enrichment is the Heavyside function with:

(21)

and . The formulation using the time stepping scheme (20) is:

(22)

in assuming that:

(23)

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 up previous contents
Next: APPLICATION TO PROBLEMS WITH Up: Second Problem: the shock Previous: The classical FEM   Contents
Renaud Merle 2000-08-26