[...]... Numerical Analysis of Differential-Algebraic Equations, P.J Rabier, W.C Rheinboldt 183 Numerical Methods for Fluids (Part 2) Mathematical Modeling and Analysis of Viscoelastic Fluids of the Oldroyd Kind, E Fern´ ndez-Cara, F Guill´ n, R.R Ortega a e 543 Volume IX Numerical Methods for Fluids (Part 3) Finite Element Methods for Incompressible Viscous Flow, R Glowinski 3 Volume X Special Volume: Computational... Numerical Methods for Solids (Part 3) Iterative Finite Element Solutions in Nonlinear Solid Mechanics, R.M Ferencz, T.J.R Hughes Numerical Analysis and Simulation of Plasticity, J.C Simo 3 183 Numerical Methods for Fluids (Part 1) NavierStokes Equations: Theory and Approximation, M Marion, R Temam 503 Contents of the Handbook xi Volume VII Solution of Equations in Rn (Part 3) Gaussian Elimination for. .. and computational mathematicians alike Finite elements and finite volumes have been the methods of choice for the numerical simulation of non-Newtonian fluid flows (see e.g., Marchal and Crochet [1986, 1987], Fortin and Fortin [1989], Fortin and Pierre [1989], El Hadj and Pa Tanguy [1990], Guenette and Fortin [1995], Fortin and Esselaoui [1987], Singh and Leal [1993], Baaijens [1994, 1998], Van Kemenade... Monte Carlo Methods for the Solution of the Schr¨ dinger o Equation for Molecular Systems, A Aspuru-Guzik, W.A Lester, Jr Linear Scaling Methods for the Solution of Schr¨ dinger’s Equation, o S Goedecker Finite Difference Methods for Ab Initio Electronic Structure and Quantum Transport Calculations of Nanostructures, J.-L Fattebert, M Buongiorno Nardelli Using Real Space Pseudopotentials for the Electronic... Methods Fluids 7 (10), 989–1145 Fortin, M., Fortin, A (1989) A new approach for the FEM simulation of viscoelastic flows J NonNewton Fluid Mech 32 (3), 295–310 Fortin, M., Pierre, R (1989) On the convergence of the mixed method of Crochet and Marchal for viscoelastic flows Comput Methods Appl Mech Eng 73 (3), 341–350 Guenette, R., Fortin, M (1995) A new mixed finite element method for computing viscoelastic... estimates that appear plausible, but for which we have yet no proof, except perhaps for very crude schemes These estimates are a crucial ingredient in the numerical analysis of several models of non-Newtonian fluids, and this analysis will remain an open question as long as such estimates are not established For this reason, the present work is dedicated only to numerical methods for the model in two dimensions... characteristics for simulation of viscoelastic fluid flow J Non-Newton Fluid Mech 36, 333–349 Fi´ tier, N., Deville, M.O (2003) Linear stability analysis of time-dependent algorithms with spece tral element methods for the simulation of viscoelastic flows J Non-Newton Fluid Mech 115 (2–3), 157–190 Fortin, M., Esselaoui, D (1987) A finite element procedure for viscoelastic flows Int J Numer Methods Fluids 7 (10),... Computing (Part 3) The Analysis of Multigrid Methods, J.H Bramble, X Zhang Wavelet Methods in Numerical Analysis, A Cohen Finite Volume Methods, R Eymard, T Gallou¨ t, R Herbin e 173 417 713 Volume VIII Solution of Equations in Rn (Part 4) Computational Methods for Large Eigenvalue Problems, H.A van der Vorst 3 Techniques of Scientific Computing (Part 4) Theoretical and Numerical Analysis of Differential-Algebraic... Paris, France E-mail: hecht@ann.jussieu.fr Numerical Methods for Non-Newtonian Fluids Copyright c 2011 Elsevier B.V Special Volume (R Glowinski and Jinchao Xu, Guest Editors) of All rights reserved HANDBOOK OF NUMERICAL ANALYSIS, VOL XVI ISSN 1570-8659 P.G Ciarlet (Editor) DOI 10.1016/B978-0-444-53047-9.00001-0 1 Contents Chapter 1 Theoretical Results 5 1.0 Foreword 5 1.1 Introduction and preliminaries... 2) Numerical Solution of Polynomial Equations, Bl Sendov, A Andreev, N Kjurkchiev 625 Volume IV Finite Element Methods (Part 2) Origins, Milestones and Directions of the Finite Element Method – A Personal View, O.C Zienkiewicz Automatic Mesh Generation and Finite Element Computation, P.L George 3 69 Numerical Methods for Solids (Part 2) Limit Analysis of Collapse States, E Christiansen Numerical Methods