On weak Dirichlet boundary conditions for elliptic problems in the continuous Galerkin method

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.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.European Union Horizon 2020US National Science Foundatio