  We present an isogeometric framework based on collocation to construct a
$C^2$-smooth approximation of the solution of the Poisson's equation over
planar bilinearly parameterized multi-patch domains. The construction of the
used globally $C^2$-smooth discretization space for the partial differential
equation is simple and works uniformly for all possible multi-patch
configurations. The basis of the $C^2$-smooth space can be described as the
span of three different types of locally supported functions corresponding to
the single patches, edges and vertices of the multi-patch domain. For the
selection of the collocation points, which is important for the stability and
convergence of the collocation problem, two different choices are numerically
investigated. The first approach employs the tensor-product Greville abscissae
as collocation points, and shows for the multi-patch case the same convergence
behavior as for the one-patch case [2], which is suboptimal in particular for
odd spline degree. The second approach generalizes the concept of
superconvergent points from the one-patch case (cf. [1, 15, 32]) to the
multi-patch case. Again, these points possess better convergence properties
than Greville abscissae in case of odd spline degree.
