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A posteriori bounds for linear functional outputs of Crouzeix-Raviart finite element discretizations of the incompressible Stokes problem

2000; Wiley; Volume: 32; Issue: 7 Linguagem: Inglês

10.1002/(sici)1097-0363(20000415)32

1097-0363

Marius Paraschivoiu, Anthony T. Patera,

Lattice Boltzmann Simulation Studies

International Journal for Numerical Methods in FluidsVolume 32, Issue 7 p. 823-849 Research Article A posteriori bounds for linear functional outputs of Crouzeix–Raviart finite element discretizations of the incompressible Stokes problem Marius Paraschivoiu, Corresponding Author marius@mie.utoronto.ca Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8===Search for more papers by this authorAnthony T. Patera, patera@mit.edu Department of Mechanical Engineering, M.I.T., Cambridge, MA 02139, U.S.A.Search for more papers by this author Marius Paraschivoiu, Corresponding Author marius@mie.utoronto.ca Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8===Search for more papers by this authorAnthony T. Patera, patera@mit.edu Department of Mechanical Engineering, M.I.T., Cambridge, MA 02139, U.S.A.Search for more papers by this author First published: 07 April 2000 https://doi.org/10.1002/(SICI)1097-0363(20000415)32:7 3.0.CO;2-ACitations: 13AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract A finite element technique is presented for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions. The finite element discretization is effected by Crouzeix–Raviart elements, the discontinuous pressure approximation of which is central to this approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic 'energy' reformulation of the desired output, the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the inter-sub-domain continuity conditions on velocity. Appealing to the dual max–min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization. The Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires the solution of only local sub-domain Stokes problems on the fine mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flow rate past and the lift force on a body immersed in a channel. Copyright © 2000 John Wiley & Sons, Ltd. Citing Literature Volume32, Issue715 April 2000Pages 823-849 RelatedInformation