A semi-smooth Newton method for solving elliptic equations with gradient constraints

Roland Griesse; Karl Kunisch

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2009)

  • Volume: 43, Issue: 2, page 209-238
  • ISSN: 0764-583X

Abstract

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Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.

How to cite

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Griesse, Roland, and Kunisch, Karl. "A semi-smooth Newton method for solving elliptic equations with gradient constraints." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 43.2 (2009): 209-238. <http://eudml.org/doc/246022>.

@article{Griesse2009,
abstract = {Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.},
author = {Griesse, Roland, Kunisch, Karl},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {gradient constraints; active set strategy; regularization; semi-smooth Newton method; primal-dual active set method; elliptic equations; numerical examples},
language = {eng},
number = {2},
pages = {209-238},
publisher = {EDP-Sciences},
title = {A semi-smooth Newton method for solving elliptic equations with gradient constraints},
url = {http://eudml.org/doc/246022},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Griesse, Roland
AU - Kunisch, Karl
TI - A semi-smooth Newton method for solving elliptic equations with gradient constraints
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2009
PB - EDP-Sciences
VL - 43
IS - 2
SP - 209
EP - 238
AB - Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
LA - eng
KW - gradient constraints; active set strategy; regularization; semi-smooth Newton method; primal-dual active set method; elliptic equations; numerical examples
UR - http://eudml.org/doc/246022
ER -

References

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  8. [8] M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13 (2002) 865–888. Zbl1080.90074MR1972219
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  10. [10] K. Ito and K. Kunisch, The primal-dual active set method for nonlinear optimal control problems with bilateral constraints. SIAM J. Contr. Opt. 43 (2004) 357–376. Zbl1077.90051MR2082706
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  12. [12] K. Kunisch and J. Sass, Trading regions under proportional transaction costs, in Operations Research Proceedings, U.M. Stocker and K.-H. Waldmann Eds., Springer, New York (2007) 563–568. Zbl1209.91149
  13. [13] O.A. Ladyzhenskaya and N.N. Ural’tseva, Linear and Quasilinear Elliptic Equations. Academic Press, New York (1968). Zbl0164.13002
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  15. [15] K. Stromberg, Introduction to Classical Real Analysis. Wadsworth International, Belmont, California (1981). Zbl0454.26001MR604364
  16. [16] G. Troianiello, Elliptic Differential Equations and Obstacle Problems. Plenum Press, New York (1987). Zbl0655.35002MR1094820
  17. [17] M. Wiegner, The C 1 , 1 -character of solutions of second order elliptic equations with gradient constraint. Comm. Partial Differ. Equ. 6 (1981) 361–371. Zbl0458.35035MR607553

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