An analogue of grad-div stabilization in nonconforming methods for incompressible flows

摘要: Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, mitigating velocity errors that are sometimes called poor mass conservation. Such arise due to the relaxation of divergence constraint methods, and excited whenever spacial discretization has deal with comparably large complicated pressures. In this contribution, an analogue grad-div presented nonconforming discretizations Discontinuous Galerkin or type. Here key penalization jumps normal velocities over facets triangulation, which controls measure-valued part distributional discrete solution. Furthermore, we characterize limit arbitrarily parameters, shows proposed remain robust accurate limit. Several numerical examples illustrate theory show their relevance simulation practical, nontrivial flows.