Abstract
A new family of coupled continuous–discontinuous Galerkin formulations is presented and analyzed in this paper. These formulations have some distinguishing properties: support to all boundary conditions, without differentiating whether the condition is Dirichlet or not; the continuous part of the formulations can use the discontinuous part to have better accuracy and robustness properties and the discontinuous part has the same stabilized properties of common discontinuous Galerkin methods. A new promising stability parameter is introduced and its effects analyzed in the numerical experiments. Some important results related to the stability of the formulations associated with the polynomial degree adopted for the continuous component are also shown.
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