hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows
Cliffe, Andrew and Hall, Edward and Houston, Paul (2012) hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows. Computers and Mathematics with Applications . ISSN 0898-1221 (Submitted)
In this article we consider the a posteriori error estimation and adaptive mesh refinement of hp-version discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the 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.
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