SIAM Journal on Mathematical Analysis
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
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
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
SIAM Journal on Scientific Computing
Editorial: High-order finite element approximation for partial differential equations
Computers & Mathematics with Applications
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We consider the application of high-order/hp-version adaptive discontinuous Galerkin finite element methods for the discretization of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Based on exploiting the Dual Weighted Residual approach, reliable and efficient a posteriori estimates of the error in the computed critical Reynolds number at which a steady pitchfork bifurcation occurs when the underlying physical system possesses either reflectional Z"2 symmetry, or rotational and reflectional O(2) symmetry, are derived. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on hp-adaptively refined computational meshes are presented for both two- and three-dimensional problems.