Grant Title: Advancements in Divergence-Free Approximations for Incompressible Flow
Michael Neilan has been recently been funded by the US National Science Foundation (award DMS 2011733) for the proposal “Advancements in Divergence-Free Approximations for Incompressible Flow” for the period of July 2020 - June 2023 . This project will construct finite element methods for the Stokes and Navier-Stokes equations that exactly enforce the divergence-free constraint at the discrete level. Such discretizations have several desirable properties, for example, improved stability and error estimates with respect to model parameters, exact conservation properties for any discretization parameter, and characterizations of discrete divergence-free subspaces.