Adaptivity and a Posteriori Error Control for Bifurcation Problems II: Incompressible Fluid Flow in Open Systems with Z (2) Symmetry

作者：Cliffe K Andrew; Hall Edward J C; Houston Paul^*; Phipps Eric T; Salinger Andrew G

来源：Journal of Scientific Computing, 2011, 47(3): 389-418.

DOI：10.1007/s10915-010-9453-3

• Incompressible flows
• Bifurcation problems
• A posteriori error estimation
• Adaptivity
• Discontinuous Galerkin methods
• Z(2) symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of 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 or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z (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 adaptively refined computational meshes are presented.

• 出版日期2011-6