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 piecewisepolynomial continuous expansion. This step allows us to identify a new weak formulation of Dirichlet boundary condition in the continuous framework. We show that the boundary condition leads to a stable discretization with a single parameter insensitive to mesh size and polynomial order of the expansion. The robustness of the approach is demonstrated on several numerical examples.
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