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Numerical zoom model multiscale problems with small defects

par Baraquin Isabelle - publié le , mis à jour le

Adnan Alahmad

I present a method numerical zoom to solve numerically model multiscale
elliptic problems with small defects using two levels of not necessarily
nested grids.
The presence of small defects modifies the solution of the multiscale
elliptic boundary value problem posed in a polygonal domain which is
perturbed at the scale $\epsilon $ about the origin $O$ in its center.

$\begin{eqnarray*} -\Delta u_{\epsilon } &=&f&\text{in }\Omega _{\epsilon } \\ u_{\epsilon } &=&0&\text{on }\partial \Omega \\ \frac{\partial u}{\partial n} &=&0&\text{on }\beta _{\epsilon } \end{eqnarray*}$

We are interested in adapting the algorithm multi-model numerical zoom to
study on model multiscale with small defects. We also give numerical
experiments of this algorithm.