Topic: Exactly divergence-free finite element methods for incompressible flows
Date of Presentation: Wednesday, January 26, 2022
Pressure-robust finite element discretizations have proven to be excellent discretization methods for incompressible flows. Pressure-robust discretizations are particularly interesting because the accuracy of the discrete velocity solution does not deteriorate as the Reynolds number is increased. In this talk, I will discuss our work on exactly divergence-free hybridizable discontinuous Galerkin (HDG) methods for incompressible flows. I will present the HDG method for the Stokes and Navier-Stokes problems and, through theory and numerical examples, show that the HDG method is pressure-robust. I will furthermore discuss a space-time extension of the HDG method for the solution of the Navier-Stokes equations on time-dependent domains.