%0 Journal Article %1 cliffe2000numerical %A Cliffe, K. A. %A Spence, A. %A Tavener, S. J. %D 2000 %I Cambridge University Press %J Acta Numerica %K 35q30-navier-stokes-equations 37k50-bifurcation-problems-for-infinite-dimensional-hamiltonian-and-lagrangian-systems 37m20-computational-methods-for-bifurcation-problems-in-dynamical-systems 65p30-numerical-problems-in-dynamical-systems-bifurcation 76d05-incompressible-navier-stokes-equations %P 39-131 %R 10.1017/S0962492900000398 %T The numerical analysis of bifurcation problems with application to fluid mechanics %U https://www.cambridge.org/core/article/numerical-analysis-of-bifurcation-problems-with-application-to-fluid-mechanics/FCF064F6E62B54C985B409E628F96A78 %V 9 %X In this review we discuss bifurcation theory in a Banach space setting using the singularity theory developed by Golubitsky and Schaeffer to classify bifurcation points. The numerical analysis of bifurcation problems is discussed and the convergence theory for several important bifurcations is described for both projection and finite difference methods. These results are used to provide a convergence theory for the mixed finite element method applied to the steady incompressible Navier–Stokes equations. Numerical methods for the calculation of several common bifurcations are described and the performance of these methods is illustrated by application to several problems in fluid mechanics. A detailed description of the Taylor–Couette problem is given, and extensive numerical and experimental results are provided for comparison and discussion.

@article{cliffe2000numerical, abstract = {In this review we discuss bifurcation theory in a Banach space setting using the singularity theory developed by Golubitsky and Schaeffer to classify bifurcation points. The numerical analysis of bifurcation problems is discussed and the convergence theory for several important bifurcations is described for both projection and finite difference methods. These results are used to provide a convergence theory for the mixed finite element method applied to the steady incompressible Navier–Stokes equations. Numerical methods for the calculation of several common bifurcations are described and the performance of these methods is illustrated by application to several problems in fluid mechanics. A detailed description of the Taylor–Couette problem is given, and extensive numerical and experimental results are provided for comparison and discussion.}, added-at = {2020-05-22T04:58:52.000+0200}, author = {Cliffe, K. A. and Spence, A. and Tavener, S. J.}, biburl = {https://www.bibsonomy.org/bibtex/2b1dbcea067175434cded26225ec5ee40/gdmcbain}, doi = {10.1017/S0962492900000398}, interhash = {1cb09d98165fa94129d2950f88e91b69}, intrahash = {b1dbcea067175434cded26225ec5ee40}, issn = {09624929}, journal = {Acta Numerica}, keywords = {35q30-navier-stokes-equations 37k50-bifurcation-problems-for-infinite-dimensional-hamiltonian-and-lagrangian-systems 37m20-computational-methods-for-bifurcation-problems-in-dynamical-systems 65p30-numerical-problems-in-dynamical-systems-bifurcation 76d05-incompressible-navier-stokes-equations}, pages = {39-131}, publisher = {Cambridge University Press}, timestamp = {2020-11-13T00:45:20.000+0100}, title = {The numerical analysis of bifurcation problems with application to fluid mechanics}, url = {https://www.cambridge.org/core/article/numerical-analysis-of-bifurcation-problems-with-application-to-fluid-mechanics/FCF064F6E62B54C985B409E628F96A78}, volume = 9, year = 2000 }