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SIAMSC
2010

Adaptive Discontinuous Galerkin Methods for Eigenvalue Problems Arising in Incompressible Fluid Flows

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Adaptive Discontinuous Galerkin Methods for Eigenvalue Problems Arising in Incompressible Fluid Flows
In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible Navier–Stokes equations. Particular attention is given to the reliable error estimation of the eigenvalue problem in channel and pipe geometries. 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 eigenvalue/stability problems. The underlying analysis consists of constructing both a dual eigenvalue problem and a dual problem for the original base solution. In this way, errors stemming from both the numerical approximation of the original nonlinear flow problem, as well as the underlying linear eigenvalue problem are correctly controlled. Numerical experiments highlighting the practical perfo...
K. Andrew Cliffe, Edward J. C. Hall, Paul Houston
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Where SIAMSC
Authors K. Andrew Cliffe, Edward J. C. Hall, Paul Houston
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