  We present a new stabilization technique for multiscale convection diffusion
problems. Stabilization for these problems has been a challenging task,
especially for the case with high Peclet numbers. Our method is based on a
constraint energy minimization idea and the discontinuous Petrov-Galerkin
formulation. In particular, the test functions are constructed by minimizing an
appropriate energy subject to certain orthogonality conditions, and are related
to the trial space. The resulting test functions have a localization property,
and can therefore be computed locally. We will prove the stability, and present
several numerical results. Our numerical results confirm that our test space
gives a good stability, in the sense that the solution error is close to the
best approximation error.
