  A finite element method for elliptic problems with discontinuous coefficients
is presented. The discontinuity is assumed to take place along a closed smooth
curve. The proposed method allows to deal with meshes that are not adapted to
the discontinuity line. The (nonconforming) finite element space is enriched
with local basis functions. We prove an optimal convergence rate in the
$H^1$--norm. Numerical tests confirm the theoretical results.
