  In this work, we apply multi-goal oriented error estimation to the finite
element method. In particular, we use the dual weighted residual method and
apply it to a model problem. This model problem consist of locally different
coercive partial differential equations in a checkerboard pattern, where the
solution is continuous across the interface. In addition to the error
estimation, the error can be localized using a partition of unity technique.
The resulting adaptive algorithm is substantiated with a numerical example.
