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 ...
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.