Title: A New Numerical Method for the Navier-Stokes Equations
The incompressible Navier-Stokes equations, which describe the motion of a viscous, incompressible, Newtonian þuid, model a wide range of problems in science and engineering. Thus, it is important to
derive efficient and high-order accurate numerical methods for this system which is challenging due to the nonlinear convective term and the incompressibility constraint. In this talk, I will focus on the approximation of the Navier-Stokes equations by the Hybridizable Discontinuous Galerkin methods which are introduced recently as an alternative to the other methods in the literature. As in the continuous case, we solve a sequence of Oseen equations in the discrete level to obtain optimal convergence for all the unknowns and a divergence-conforming, divergence-free velocity which superconverges.