Application of hp–Adaptive Discontinuous Galerkin Methods to Bifurcation Phenomena in Pipe Flows
- 1.7k Downloads
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 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.
KeywordsDual Weighted Residual (DWR) Discontinuous Galerkin ﬁnite Element Approximation Posteriori Error Estimates Interior Penalty Discontinuous Galerkin Method Symmetry Breaking Bifurcation
- 3.Brezzi, F., Rappaz, J., Raviart, P.: Finite dimensional approximation of non-linear problems.3.Simple bifurcation points.Numer.Math.38(1), 1–30 (1981)Google Scholar
- 7.Cliffe, K., Hall, E., Houston, P., Phipps, E., Salinger, A.: Adaptivity and a posteriori error control for bifurcation problems III: Incompressible fluid flow in open systems with O(2) symmetry.J.of Sci.Comput.52(1), 153–179 (2012).In pressGoogle Scholar