Séance Séminaire

NEMESIS Seminar

From Discontinuous Galerkin Enrichment to General Criteria for Discrete de Rham Complexes

We first discuss enrichment strategies preserving cohomology for discontinuous Galerkin de Rham complexes. In this setting, higher-order spaces are viewed as cohomologically consistent enrichments of a lowest-order complex, provided that simple assumptions are verified. We then move towards simple criteria for the construction of discrete de Rham complexes. The proposed perspective relies on local exactness, interface complexes, compatible trace and restriction operators, and a weak discrete Mayer-Vietoris argument. The latter is chosen so that the construction is compatible with both « discontinuous » and « continuous « complexes. This gives a possible route to generalize the DG enrichment criterion and to compare DG, DDR, and compatible VEM constructions within a common homological framework.