Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flowsTools Cliffe, Andrew, Hall, Edward and Houston, Paul (2013) Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows. In: Numerical Mathematics and Advanced Applications, ENUMATH 2011, 5-9 September 2011, Leicester, UK. Full text not available from this repository.AbstractIn 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 rotational and reflectional or O(2) symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual Weighted Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on hp-adaptively refined computational meshes are presented.
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