Pressure- and Reynolds-semi-robust space-time DG methods for the incompressible Navier-Stokes equations

In this talk, we present the main ideas for the analysis of a space-time DG method for the incompressible Navier-Stokes equations. This method combines an H(div)-conforming DG spatial discretization with a DG time-stepping scheme, and we show that it is both pressure robust and Reynolds semi-robust. Proving stability and convergence for high-order approximations requires nonstandard techniques. We overcome this challenge using carefully chosen test functions, establishing well-posedness, unconditional stability, and quasi-optimal error estimates (even for high Reynolds numbers). Finally, we present numerical experiments that validate the robustness and accuracy of the method.