Roland Glowinski published 8 books and more than 300 articles. He was also an editor of many very well cited proceedings. Hence this attempt to summarize his scientific work is not likely to do justice to his work. Nevertheless, we will try to extract his major contributions, such as the augmented Lagrangian algorithm, various domain decomposition and fictitious methods and their performance on the Navier–Stokes equations in a moving domain. Roland has created a school of applied mathematicians remarkable by their rigor and efficiency for industrial applications. He marked his time and his books will be authorities as long as computer architectures are similar to their present structures.
Roland Glowinski a publié 8 livres et plus de 300 articles. Il a également été rédacteur en chef de nombreux actes très bien cités. Il est donc peu probable que cette tentative de résumer son travail scientifique rende justice à son œuvre. Néanmoins, nous essaierons d’extraire ses principales contributions, telles que l’algorithme du Lagrangien augmenté, diverses méthodes de décomposition de domaines et méthodes de domaines fictifs et leurs performances sur les équations de Navier–Stokes dans un domaine mobile. Roland a créé une école de mathématiciens appliqués remarquables par leur rigueur et leur efficacité pour les applications industrielles. Il a marqué son temps et ses livres feront autorités tant que la structure des ordinateurs restera ce qu’elle est actuellement.
Revised:
Accepted:
Online First:
Published online:
Mots-clés : Méthode des éléments finis, gradient conjugiué, équations de Navier–Stokes, fluide non-newtonien, domaine fictif, décomposition de domaine
Alain Bensoussan 1, 2; Olivier Pironneau 3

@article{CRMECA_2023__351_S1_73_0, author = {Alain Bensoussan and Olivier Pironneau}, title = {The {Legacy} of {Roland} {Glowinski}}, journal = {Comptes Rendus. M\'ecanique}, pages = {73--88}, publisher = {Acad\'emie des sciences, Paris}, volume = {351}, number = {S1}, year = {2023}, doi = {10.5802/crmeca.169}, language = {en}, }
Alain Bensoussan; Olivier Pironneau. The Legacy of Roland Glowinski. Comptes Rendus. Mécanique, The scientific legacy of Roland Glowinski, Volume 351 (2023) no. S1, pp. 73-88. doi : 10.5802/crmeca.169. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.169/
[1] Numerical Methods for Nonlinear Variational Problems, Springer Series in Computational Physics, Springer, 1984 | DOI | Zbl
[2] Etude et approximation de quelques problèmes intégraux et intégro-differentiels, Ph. D. Thesis, Université Paris VI, Paris, France (1970)
[3] Resolution numérique d’un probleme non classique de calcul des variations, Symposium on Optimization, Nice 1969 (A. V. Balakrisnan, ed.) (Lecture Notes in Mathematics), Volume 132, Springer (1970), pp. 108-129 | Zbl
[4] The Finite Element Method for Elliptic Problems, Studies in Mathematics and its Applications, 4, North-Holland, 1978 | Zbl
[5] Sur des méthode d’optimisation par relaxation, Rev. Franc. Automat. Inform. Rech. Operat., Volume 7 (1973) no. R-3, pp. 5-32 | Zbl
[6] Semi-smooth Newton methods for variational inequalities of the first kind, M2AN, Math. Model. Numer. Anal., Volume 37 (2003) no. 1, pp. 41-62 | Numdam | MR | Zbl
[7] Numerical study of a dual iterative method for solving a finite element approximation of the biharmonic equation, Computer Methods appl. Mech. Engin., Volume 9 (1976), pp. 203-218 | DOI | MR | Zbl
[8] Finite Element Analysis of the unsteady flow of a visco-plastic fluid in a cylindrical pipe, Finite Element Methods in Flow Problems (J. T. Oden; O. C. Zienkiewicz; R. H. Gallagher; C. Taylor, eds.), University of Alabama Press, Huntsville (1974), pp. 471-488
[9] Analyse numérique du champs magnétique d’un alternateur par éléments finis, Comput. Methods Appl. Mech. Engin., Volume 3 (1974) no. 1, pp. 55-85 | DOI | Zbl
[10] Dual numerical techniques, application to an optimal control problem, Techniques in Optimization (A. V. Balakrishnan, ed.) (1972), pp. 159-174
[11] Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem, SIAM Rev., Volume 21 (1979) no. 2, pp. 167-212 | DOI | MR | Zbl
[12] Resolution of the implicit Euler scheme for the Navier–Stokes equation through a least-squares method (To appear in Numerisch Mathematik, https://hal.archives-ouvertes.fr/hal-01996429/)
[13] Application of Optimal Control and Finite Element Methods to the Calculation of Transonic Flows and Incompressible Viscous Flows, Numerical methods in applied fluid dynamics (Reading, 1978), Academic Press Inc., 1980, pp. 203-320 | Zbl
[14] Méthodes de lagrangien augmenté: applications à la résolution numérique de problèmes aux limites, Méthodes mathématiques de l’Informatique, 9, Dunod; North-Holland, 1982
[15] Analyse Numérique des inéquation variationnelles, Méthodes Mathématiques de l’Informatique, 5, Bordas-Dunod, 1976 | Zbl
[16] Finite Element Methods for Incompressible Viscous Flow, Numerical methods for fluids (Part 3) (P. G. Ciarlet; J. L. Lions, eds.) (Handbook of Numerical Analysis), Volume 9, North-Holland, 2003, pp. 1-1083 | Zbl
[17] Numerical simulation of incompressible viscous flow, De Gruyter Series in Applied and Numerical Mathematics, 7, Walter de Gruyter, 2022 | DOI | Zbl
[18] Error analysis of a fictitious domain method ap- plied to a Dirichlet problem, Japan J. Ind. Appl. Math., Volume 12 (1995) no. 3, pp. 487-514 | DOI | Zbl
[19] Augmented Lagrangians and Operator Splitting Methods in Nonlinear Mechanics, SIAM Studies in Applied Mathematics, 9, Society for Industrial and Applied Mathematics, 1989 | DOI | Zbl
[20] Numerical Methods for Nonlinear Problems in Fluid Dynamics, Supercomputing (A. Lichnewsky; C. Saguez, eds.), North-Holland (1987), pp. 381-479 | Zbl
[21] Fluid-particle flow: a symmetric formulation, C. R. Math. Acad. Sci. Paris, Volume 324 (1997) no. 9, pp. 1079-1084 | DOI | MR | Zbl
[22] Operator Splitting, Splitting Methods in Communication, Imaging, Science, and Engineering (Scientific Computation), Springer, 2016, pp. 95-114 | DOI | Zbl
[23] Efficient iterative solvers for elliptic finite element problems on nonmatching grids, Russ. J. Numer. Anal. Math. Model., Volume 10 (1995) no. 3, pp. 187-211 | MR | Zbl
[24] A fictitious domain method with Lagrange multipliers, ENUMATH 99. Numerical mathematics and advanced applications. Proceedings of the 3rd European conference, Jyväskylä, Finland, July 26-30, 1999 (Neittaanmaki; T. Tiihonen; P. Tarvainen, eds.), World Scientific (2000), pp. 733-742 | Zbl
[25] Fictitious domain and domain decomposition methods, Sov. J. Numer. Anal. Math. Model., Volume 1 (1986) no. 1, pp. 3-35 | MR | Zbl
[26] Domain decomposition methods for large linearly elliptic three dimensional problems (1990) no. RR-1182 (https://hal.inria.fr/inria-00075376) (Technical report)
[27] A distributed Lagrange multiplier/fictitious domain method for flow around moving rigid bodies: Application to particulate flow, Int. J. Numer. Methods Fluids, Volume 30 (1999) no. 8, pp. 1043-1066 | DOI | Zbl
[28] A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow, Volume 25 (1999) no. 5, pp. 755-794 | DOI | MR | Zbl
[29] A 3D DLM/FD method for simulating the motion of spheres in a bounded shear flow of Oldroyd-B fluids, Comput. Fluids, Volume 172 (2018), pp. 661-673 | DOI | MR | Zbl
Cited by Sources:
Comments - Policy