hp-adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows

We consider the application of high-order/hp-version adaptive discontinuous Galerkin finite element methods for the discretization of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Based on exploiting the Dual Weighted Residual approach, reliable and efficient a posteriori estimates of the error in the computed critical Reynolds number at which a steady pitchfork bifurcation occurs when the underlying physical system possesses either reflectional Z"2 symmetry, or rotational and reflectional O(2) symmetry, are derived. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on hp-adaptively refined computational meshes are presented for both two- and three-dimensional problems.