Mathematics of Computation
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Local Discontinuous Galerkin Methods for the Stokes System
SIAM Journal on Numerical Analysis
Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Mixed hp-DGFEM for Incompressible Flows
SIAM Journal on Numerical Analysis
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations
Journal of Computational Physics
A Convergent Adaptive Method for Elliptic Eigenvalue Problems
SIAM Journal on Numerical Analysis
Benchmark results for testing adaptive finite element eigenvalue procedures
Applied Numerical Mathematics
An iterative adaptive finite element method for elliptic eigenvalue problems
Journal of Computational and Applied Mathematics
hp-adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows
Computers & Mathematics with Applications
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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 and the underlying linear eigenvalue problem are correctly controlled. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.