Adaptivity and a posteriori error control for bifurcation problems. III: Incompressible fluid flow in open systems with \(O(2)\) symmetry

DOI10.1007/s10915-011-9545-8zbMath1311.76053OpenAlexW4246970173MaRDI QIDQ1930930

Paul Houston, Andrew G. Salinger, Edward J. C. Hall, K. Andrew Cliffe, Eric T. Phipps

Publication date: 14 January 2013

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-011-9545-8

zbMATH Keywords

incompressible flowsadaptivitydiscontinuous Galerkin methodsbifurcation problems\(O(2)\) symmetrya \(posteriori\) error estimation

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items

\(hp\)-adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows, A localized reduced-order modeling approach for PDEs with bifurcating solutions, On the application of reduced basis methods to bifurcation problems in incompressible fluid dynamics, $hp$-Adaptive Discontinuous Galerkin Methods for Neutron Transport Criticality Problems, Adaptivity and a posteriori error control for bifurcation problems. II: Incompressible fluid flow in open systems with \(Z_{2}\) symmetry, Turbulent models of oil flow in a circular pipe with sudden enlargement, Discretization and perturbations in the simulation of localized turbulence in a pipe with a sudden expansion

Uses Software

• FreeFem++
• MUMPS
• ARPACK

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
• Finite dimensional approximation of nonlinear problems. III: Simple bifurcation points
• Adaptivity and a posteriori error control for bifurcation problems. II: Incompressible fluid flow in open systems with \(Z_{2}\) symmetry
• Singularities and groups in bifurcation theory. Volume I
• Singularities and groups in bifurcation theory. Volume II
• Multifrontal parallel distributed symmetric and unsymmetric solvers
• Eigenvalues of the discretized Navier-Stokes equation with application to the detection of Hopf bifurcations
• Adaptive Discontinuous Galerkin Methods for Eigenvalue Problems Arising in Incompressible Fluid Flows
• Analysis and Computation of Symmetry-Breaking Bifurcation and Scaling Laws Using Group-Theoretic Methods
• The Computation of Symmetry-Breaking Bifurcation Points
• An optimal control approach to a posteriori error estimation in finite element methods
• Convective instability and transient growth in steady and pulsatile stenotic flows
• ARPACK Users' Guide
• The local discontinuous Galerkin method for the Oseen equations
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Local Discontinuous Galerkin Methods for the Stokes System
• A locally conservative LDG method for the incompressible Navier-Stokes equations
• O(2)-symmetry breaking bifurcation: with application to the flow past a sphere in a pipe
• Adaptivity and a Posteriori Error Control for Bifurcation Problems I: the Bratu Problem
• Bifurcation phenomena in the flow through a sudden expansion in a circular pipe
• Three-dimensional instabilities and transition of steady and pulsatile axisymmetric stenotic flows