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Variational Methods for Numerical Solution of Nonlinear Elliptic Problems [Minkštas viršelis]

  • Formatas: Paperback / softback, 481 pages, aukštis x plotis x storis: 229x152x28 mm, weight: 947 g, illustrations
  • Serija: CBMS-NSF Regional Conference Series in Applied Mathematics 86
  • Išleidimo metai: 30-Oct-2015
  • Leidėjas: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611973775
  • ISBN-13: 9781611973778
Kitos knygos pagal šią temą:
Variational Methods for Numerical Solution of Nonlinear Elliptic ProblemsDidesnis paveikslėlis
  • Formatas: Paperback / softback, 481 pages, aukštis x plotis x storis: 229x152x28 mm, weight: 947 g, illustrations
  • Serija: CBMS-NSF Regional Conference Series in Applied Mathematics 86
  • Išleidimo metai: 30-Oct-2015
  • Leidėjas: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611973775
  • ISBN-13: 9781611973778
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781611973778.html
Raktažodžiai:
After writing three books on applying variational methods to problems from science and engineering, Glowinski recently became interested in the numerical solution of nonlinear elliptic problems, and so describes how to use variational methods to solve them as well. He covers some variational problems in Hilbert spaces, iterative methods in Hilbert spaces, operator-splitting and alternating directions methods, augmented Lagrangians and alternating direct methods of multipliers, the least-squares solution of linear and nonlinear problems, obstacle problems and Bingham flow with applications to control, nonlinear eigenvalue problems, Eikonal equations, and fully nonlinear elliptic equations. Annotation ©2016 Ringgold, Inc., Portland, OR (protoview.com)

A detailed insight into computational methods for efficient solution of nonlinear elliptic problems, for advanced graduates and researchers.

Daugiau informacijos

A detailed insight into computational methods for efficient solution of nonlinear elliptic problems, for advanced graduates and researchers.
Preface xv
Chapter 1 On Some Variational Problems in Hilbert Spaces
1(68)
1.1 Introduction
1(1)
1.2 A particular class of linear variational problems in Hilbert spaces
1(45)
1.3 On variational inequalities in Hilbert spaces. (I) Elliptic variational inequalities of the first kind
46(10)
1.4 On variational inequalities in Hilbert spaces. (II) Elliptic variational inequalities of the second kind
56(13)
Chapter 2 Iterative Methods in Hilbert Spaces
69(44)
2.1 Introduction. Synopsis
69(1)
2.2 On Newton's method
70(11)
2.3 Conjugate gradient algorithms
81(31)
2.4 Further comments on iterative methods
112(1)
Chapter 3 Operator-Splitting and Alternating Direction Methods
113(44)
3.1 Introduction. Synopsis
113(1)
3.2 On alternating direction--type methods
114(22)
3.3 On Lie's and Strang's operator-splitting schemes
136(8)
3.4 Applications
144(13)
Chapter 4 Augmented Lagrangians and Alternating Direction Methods of Multipliers
157(46)
4.1 Introduction. Synopsis
157(1)
4.2 A historical perspective
158(7)
4.3 Decomposition-coordination methods by augmented Lagrangians
165(5)
4.4 A convex finite dimensional application: The numerical solution of the Weber problem
170(2)
4.5 Application to the solution of a nonconvex problem from nonlinear elasticity
172(6)
4.6 Application to the solution of the Dirichlet problem for the two-dimensional elliptic Monge--Ampere equation
178(10)
4.7 Application to the solution of a nonsmooth eigenvalue problem from visco-plasticity
188(13)
4.8 Further comments. References
201(2)
Chapter 5 Least-Squares Solution of Linear and Nonlinear Problems in Hilbert Spaces
203(34)
5.1 Generalities
203(6)
5.2 Least-squares conjugate gradient solution of nonlinear problems in Hilbert spaces
209(15)
5.3 Least-squares conjugate gradient solution of linear problems in Hilbert spaces
224(12)
5.4 Further comments and references
236(1)
Chapter 6 Obstacle Problems and Bingham Flow: Application to Control
237(48)
6.1 Introduction. Synopsis
237(1)
6.2 A penalty/Newton/conjugate gradient method for the solution of obstacle problems for linear second order elliptic operators
238(8)
6.3 A penalty/Newton/conjugate gradient method for the simulation of Bingham flows in cylinders
246(22)
6.4 Application to the optimal control of distributed parameter systems modeled by parabolic variational inequalities of the obstacle type
268(14)
6.5 Further comments on penalty methods
282(3)
Chapter 7 2u = λu3 and Other Nonlinear Eigenvalue Problems
285(68)
7.1 Introduction. Synopsis
285(2)
7.2 Numerical solution of the Lane--Emden problem (7.1)
287(34)
7.3 On the numerical solution of the steady von Karman equations for nonlinear elastic thin plates
321(16)
7.4 On the numerical solution of a nonsmooth eigenvalue problem from visco-plasticity
337(6)
7.5 A variant of the Bratu problem: Vortex condensation in the Chern--Simons Higgs model
343(10)
Chapter 8 Eikonal Equations
353(26)
8.1 Introduction. Synopsis
353(1)
8.2 A calculus-of-variations approach to the solution of (8.1)
354(1)
8.3 An equivalent variational formulation of problem (8.9). An associated initial value problem
355(1)
8.4 Time discretization of problem (8.15) by operator splitting
356(2)
8.5 Finite element implementation
358(2)
8.6 On the Eikonal equation |u| = 1
360(5)
8.7 Numerical experiments
365(5)
8.8 Further comments
370(9)
Chapter 9 Fully Nonlinear Elliptic Equations
379(42)
9.1 Introduction. Synopsis
379(1)
9.2 On the least-squares solution of the Dirichlet problem for the elliptic Monge--Ampere equation in dimension 2
380(24)
9.3 A least-squares/operator-splitting method for solving the Dirichlet problem for a two-dimensional elliptic Pucci equation
404(17)
Epilogue 421(4)
Bibliography 425(24)
Author Index 449(6)
Subject Index 455
Roland Glowinski is Cullen Professor of Mathematics at the University of Houston and an Emeritus Professor of the Université Pierre et Marie Curie (Paris VI). He is a member of the French National Academy of Sciences, the French National Academy of Technology, and the Academia Europaea. He is also a Fellow of both SIAM and the AMS and past recipient of the Theodore von Kįrmįn Prize for the notable application of mathematics to mechanics and/or the engineering sciences.