A Reynolds-semi-robust H-div conforming method for unsteady incompressible power-law flows
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In this talk, we will present a Reynolds-quasi-robust and pressure-robust velocity finite element method for an Hdiv-conforming approximation of the unsteady incompressible Navier-Stokes equation with power-law type constitutive law. The proposed methods hinges on a discontinuous Galerkin approximation of the viscous term and a reinforced upwind-type stabilization of the convective term. The derived velocity error estimates account for pre-asymptotic orders of convergence observed in convection-dominated flows through regimedependent estimates of the error contributions, underlining the interplay among the two nonlinear terms of convection and p-diffusion. After introducing the method, we will present the theoretical results and finally show a set of numerical tests.
