  We combine continuous and discontinuous Galerkin methods in the setting of a
model diffusion problem. Starting from a hybrid discontinuous formulation, we
replace element interiors by more general subsets of the computational domain -
groups of elements that support a piecewise-polynomial continuous expansion.
This step allows us to identify a~new weak formulation of Dirichlet boundary
condition in the continuous framework. We examine the expected performance of a
Galerkin solver that would use continuous Galerkin method with weak Dirichlet
boundary conditions in each mesh partition and connect partitions weakly using
trace variable as in HDG method.
