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3. Channel Flow.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

In this chapter, we consider a steady, two-dimensional, incompressible, laminar channel flow of a viscous fluid. At high Reynolds numbers, small wall perturbations, such as indentations, can generate adverse pressure gradients leading to flow separation. In a channel, there is no external flow region and the asymptotic models for the flow perturbations are mainly based on an inviscid rotational core flow region together with boundary layers near the walls; a comprehensive discussion of this structure can be found in Sobey [94]. The asymptotic analysis of these flows has been performed essentially by Smith [89, 90, 91, 92] and a systematic approach has been proposed later by Saintlos and Mauss [85]. More recently, the modelling of channel flow has been examined by Lagrée et al. [49] and by Lagrée and Lorthois [50]. [ABSTRACT FROM AUTHOR]

Published
2007
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4. Turbulent Boundary Layer.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

The three-dimensional unsteady Navier-Stokes equations given in Appendix I also apply to turbulent flow if the values of dependent variables are understood as instantaneous values. A direct approach to solving the equations for turbulent flows is to solve them for specific boundary conditions and initial values that include time-dependent quantities. Mean values are needed in most practical cases, so an ensemble of solutions of time-dependent equations is required. Even for the most restricted cases, this approach, referred to as direct numerical simulation, becomes a difficult and extremely expensive computing problem because the unsteady eddy motions of turbulence appear over a wide range. The usual procedure is to average the equations rather than their solutions [77]. The averaged Navier-Stokes equations are also called Reynolds equations. This procedure is used here to study the turbulent boundary layer. [ABSTRACT FROM AUTHOR]

Published
2007
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5. Regular Forms of Interactive Boundary Layer.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

In Chap. 8, the application of the successive complementary expansion method, SCEM, to high Reynolds number flows past streamlined bodies led us to the notion of interactive boundary layer, IBL, to first and to second order. The salient feature of IBL is to ensure the interaction between the equations describing the inviscid and viscous flows. [ABSTRACT FROM AUTHOR]

Published
2007
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6. Applications of Interactive Boundary Layer Models.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

The successive complementary expansion method, SCEM, in its generalized form, fully justifies the notion of IBL. A UVA is obtained by solving two sets of equations — the generalized boundary layer equations and the inviscid flow equations. These two systems are strongly coupled. In the framework of the standard boundary layer theory, a hierarchy is established between the two systems: first, we can solve the inviscid flow equations and then the boundary layer equations. With IBL, this hierarchy is broken; the two systems interact, one system influences the other and vice versa. [ABSTRACT FROM AUTHOR]

Published
2007
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7. Interactive Boundary Layer.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

The method of matched asymptotic expansions, MMAE, has been extensively used in fluid mechanics and contributed to the remarkable advances in the description of flows [107]. The study of high Reynolds number flows past streamlined bodies is one of the most famous example. [ABSTRACT FROM AUTHOR]

Published
2007
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8. High Reynolds Number Flows.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

As an introduction to the second part of this book devoted to the asymptotic analysis of high Reynolds number flows, this Chapter reminds standard results which are useful subsequently for the general understanding of the subject. Then, most of these results are given without detailed proof. [ABSTRACT FROM AUTHOR]

Published
2007
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9. Ordinary Differential Equations.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

The practical implementation of the successive complementary expansion method, SCEM, is presented in this Chapter with applications to functions implicitly defined as solutions of ordinary differential equations. In all the cases, the solution depends on a small parameter leading to a singular perturbation problem. More precisely, the structure of the solution exhibits a boundary layer. The boundary layer is always located in the neighbourhood of a singular point, but this point is not necessarily a part of the boundary of the considered domain. Among the variety of examples found in the literature [17, 42, 48, 72], a selection has been made to enlighten the various aspects of SCEM and its advantages. This is a first step toward the treatment of physical problems governed by partial differential equations. [ABSTRACT FROM AUTHOR]

Published
2007
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10. Successive Complementary Expansion Method.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

This chapter is devoted to the asymptotic analysis of singular functions. Two versions of the method of matched asymptotic expansions, MMAE, are reminded with their advantages and drawbacks. The first method, associated with the intermediate matching, is the most popular one since it is apparently the most natural one. The second method, based on Van Dyke's matching principle, VDP, is more puzzling but its application is easier. In both methods, the point is to match two approximations defined in contiguous domains. VDP enables us to understand how a composite approximation, which is taken as a uniformly valid approximation, UVA, can be constructed. This analysis leads us to a modified Van Dyke principle, MVDP, which seems to solve the known counter-examples to VDP, in particular when logarithms are present. This latter method suggests a new approach which is called the successive complementary expansion method, SCEM. The regular form of SCEM is equivalent to MMAE but sets us free of any asymptotic matching. Moreover, the general form of SCEM, with the use of generalized asymptotic expansions, AEs, enables us to treat problems which cannot be solved in an easy manner with regular expansions. [ABSTRACT FROM AUTHOR]

Published
2007
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11. Asymptotic Expansions.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

This chapter describes the main tools for asymptotic expansions. In particular, an expansion depends on the use of an asymptotic sequence formed from order functions. Different approaches can be used but, keeping in mind we are interested in practical methods, we use a set of order functions for which a total ordering exists. A more in-depth study can be found in the book by Eckhaus [33]. [ABSTRACT FROM AUTHOR]

Published
2007
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12. Boundary Layer Structure.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

The singular perturbation problems considered in this Chapter are based on second order linear differential equations with variable coefficients. We are interested in boundary value problems because not only local existence theorems do not exist but also because these problems are more difficult to treat than initial value problems. Moreover, the solution is not known analytically. Finally if, for a well-posed physical problem, it is relatively easy to localize the domain of non-uniformity, this is not the case here because the problem is purely mathematical. The abstract formulation of the problem does not enable us to determine, a priori, the localization of the boundary layer. The method described in this Chapter to localize the boundary layer is standard and can be used as a good guide for more complex problems. [ABSTRACT FROM AUTHOR]

Published
2007
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13. Introduction to Singular Perturbation Problems.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

Mathematical models used in physics often lead to problems which do not have explicit solutions. Their numerical solutions become more difficult when small parameters are present or when the calculation domains are very large. In such cases, simpler models can be developed either by setting a parameter to zero or by restricting the study to a smaller domain. When a small parameter, denoted by ɛ, is set to zero, it is possible that the solution of the initial problem does not tend uniformly to the solution of the reduced problem as ɛ → 0. A singular perturbation problem arises for which difficult mathematical questions need to be addressed. [ABSTRACT FROM AUTHOR]

Published
2007
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14. Introduction.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

The history of relations between science and technique is surprising and stormy just like those of a couple combining love, hatred and necessity. Obviously, we can go into ecstasies over the marvels obtained by the thought in the study of motion from Aristotle to Einstein, passing by Galileo, Newton and Laplace. We can be also attracted by the successes of technique from the wheel to the computer passing by the astronomical telescope and the aircraft. Beyond the secular questioning about the pre-eminence of one on the other, are not science and technique the two faces of intelligence and reason? [ABSTRACT FROM AUTHOR]

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2007
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15. Geometry of Curves.

Author

Chattot, J.-J., Colella, P., Weinan, E., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Liseikin, Vladimir D.

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2007
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16. Numerical Implementation of Grid Generators.

Author

Chattot, J.-J., Colella, P., Weinan, E., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Liseikin, Vladimir D.

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2007
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17. Inverted Equations.

Author

Chattot, J.-J., Colella, P., Weinan, E., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Liseikin, Vladimir D.

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2007
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18. Comprehensive Grid Models.

Author

Chattot, J.-J., Colella, P., Weinan, E., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Liseikin, Vladimir D.

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2007
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19. Multidimensional Geometry.

Author

Chattot, J.-J., Colella, P., Weinan, E., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Liseikin, Vladimir D.

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2007
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20. General Coordinate Systems in Domains.

Author

Chattot, J.-J., Colella, P., Weinan, E., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Liseikin, Vladimir D.

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2007
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21. Introductory Notions.

Author

Chattot, J.-J., Colella, P., Weinan, E., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Liseikin, Vladimir D.

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2007
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22. Spectral Methods Primer.

Author

Chattot, J. -J., Colella, P., E, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Canuto, Claudio, and Quarteroni, Alfio

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2007
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23. General Algorithms for Incompressible Navier-Stokes Equations.

Author

Chattot, J. -J., Colella, P., E, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Canuto, Claudio, and Quarteroni, Alfio

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2007
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24. Solution Strategies for Spectral Methods in Complex Domains.

Author

Chattot, J. -J., Colella, P., E, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Canuto, Claudio, and Quarteroni, Alfio

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2007
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29. Fundamentals of Fluid Dynamics.

Author

Chattot, J. -J., Colella, P., E, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Canuto, Claudio, and Quarteroni, Alfio

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2007
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30. Semiconductor Modeling.

Author

Chattot, J.-J., Colella, P., Weinan, E, Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Chen, Zhangxin

Published
2005
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31. Fluid Flow in Porous Media.

Author

Chattot, J.-J., Colella, P., Weinan, E, Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Chen, Zhangxin

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2005
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32. Mixed Finite Elements.

Author

Chattot, J.-J., Colella, P., Weinan, E, Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Chen, Zhangxin

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2005
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33. Elementary Finite Elements.

Author

Chattot, J.-J., Colella, P., Weinan, E, Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Chen, Zhangxin

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2005
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34. Adaptive Finite Elements.

Author

Chattot, J.-J., Colella, P., Weinan, E, Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Chen, Zhangxin

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2005
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35. Fluid Mechanics.

Author

Chattot, J.-J., Colella, P., Weinan, E, Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Chen, Zhangxin

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2005
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36. Discontinuous Finite Elements.

Author

Chattot, J.-J., Colella, P., Weinan, E, Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Chen, Zhangxin

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2005
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37. Characteristic Finite Elements.

Author

Chattot, J.-J., Colella, P., Weinan, E, Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Chen, Zhangxin

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2005
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38. Nonconforming Finite Elements.

Author

Chattot, J.-J., Colella, P., Weinan, E, Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Chen, Zhangxin

Published
2005
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39. Decomposition-Coordination Methods by Augmented Lagrangian: Applications.

Author

Chattot, J. -J., Colella, P., E., W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Glowinski, Roland

Abstract

A large number of problems in mathematics, physics, mechanics, economics, etc. may be formulated as P$$ \mathop {Min}\limits_{v \in V} \{ F(Bv) + G(v)\} $$ where V, H are topological vector spacesB ∈ ℒ (V, H)F: H → $$ \bar {\mathbb{R}} $$ , G:V → $$ \bar {\mathbb{R}} $$ are convex proper l.s.c. functionals. [ABSTRACT FROM AUTHOR]

Published
1984
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40. Least-Squares Solution of Nonlinear Problems: Application to Nonlinear Problems in Fluid Dynamics.

Author

Chattot, J. -J., Colella, P., E., W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Glowinski, Roland

Abstract

In this chapter we would like to discuss the solution of some nonlinear problems in fluid dynamics by a combination of least-squares, conjugate gradient, and finite element methods. In view of introducing the reader to this technical subject, we consider in Sec. 2 the solution of systems of nonlinear equations in ℝN by least-squares methods; then, in Sec. 3, the solution of a nonlinear Dirichlet model problem; also in Sec. 3 we make some comments about the use of pseudo-arc-length-continuation methods for solving nonlinear problems. [ABSTRACT FROM AUTHOR]

Published
1984
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41. Relaxation Methods and Applications.

Author

Chattot, J. -J., Colella, P., E., W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Glowinski, Roland

Abstract

The key idea of relaxation methods is to reduce, using some iterative process, the solution of some problems posed in a product space V=∏i=1NVi (minimization of functionals, solution of systems of equations and/or inequalities, etc.) to the solution of a sequence of subproblems of the same kind, but simpler, since they are posed in the Vi. [ABSTRACT FROM AUTHOR]

Published
1984
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42. Applications of Elliptic Variational Inequality Methods to the Solution of Some Nonlinear Elliptic Equations.

Author

Chattot, J. -J., Colella, P., E., W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Glowinski, Roland

Abstract

For solving some nonlinear elliptic equations, it may be convenient, from the theoretical and numerical points of view, to view them as EVI's. [ABSTRACT FROM AUTHOR]

Published
1984
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43. On the Approximation of Parabolic Variational Inequalities.

Author

Chattot, J. -J., Colella, P., E., W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Glowinski, Roland

Abstract

In this chapter we would like to give some indications of the approximation of parabolic variational inequalities (PVI) (mostly without proof). For a detailed reference, see Fortin [1], Bristeau [1], Bristeau and Glowinski [1], C. Johnson [1], and A. Berger [1].1 See also Richtmyer and Morton [1], Kreiss [1], and Lascaux [1] for the numerical analysis of time-dependent equations. [ABSTRACT FROM AUTHOR]

Published
1984
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44. Application of the Finite Element Method to the Approximation of Some Second-Order EVI.

Author

Chattot, J. -J., Colella, P., E., W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Glowinski, Roland

Abstract

In this chapter we consider some examples of EVI of the first and second kinds. These EVI are related to second-order partial differential operators (for fourth-order problems, see Glowinski [2] and G.L.T. [2], [3]). The physical interpretation and some properties of the solution are given. Finite element approximations of these EVI are considered and convergence results are proved. In some particular cases we also give error estimates. [ABSTRACT FROM AUTHOR]

Published
1984
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45. Generalities on Elliptic Variational Inequalities and on Their Approximation.

Author

Chattot, J. -J., Colella, P., E., W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., and Glowinski, Roland

Abstract

An important and very useful class of nonlinear problems arising from mechanics, physics, etc. consists of the so-called variational inequalities. We consider mainly the following two types of variational inequalities, namely: 1.elliptic variational inequalities (EVI),2.parabolic variational inequalities (PVI). [ABSTRACT FROM AUTHOR]

Published
1984
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46. Conclusion.

Author

Chattot, J. -J., Colella, P., Eist, W., Glowinski, R., Holt, M., Hussaini, Y., Joly, P., Keller, H. B., Marsden, J. E., Meiron, D. I., Pironneau, O., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J. H., Szepessy, A., Wheeler, M. F., Cousteix, Jean, and Mauss, Jacques

Abstract

This book contains two distinct parts. [ABSTRACT FROM AUTHOR]

Published
2007
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