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**Two-sided approximations for unilateral variational inequalities by multi-grid methods.**
*(English)*
Zbl 0635.49006

In this interesting and well written article for the numerical solution of unilateral variational inequalities two iterative schemes are developed which provide approximations from below resp. from above. Both schemes are based on some kind of active set strategy and require the solution of an algebraic system of equations at each iteration step which is done by means of multigrid techniques. Convergence results are established and illustrated by some numerical results for the elastic- plastic torsion problem.

Related results have been obtained in the author’s article in SIAM J. Numer. Anal. 24, 1046-1065 (1987; Zbl 0628.65046).

Related results have been obtained in the author’s article in SIAM J. Numer. Anal. 24, 1046-1065 (1987; Zbl 0628.65046).

Reviewer: P.Neitaanmäki

### MSC:

49J40 | Variational inequalities |

49M25 | Discrete approximations in optimal control |

65K10 | Numerical optimization and variational techniques |

35J85 | Unilateral problems; variational inequalities (elliptic type) (MSC2000) |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

### Keywords:

two-sided approximation; unilateral variational inequalities; active set strategy; multigrid techniques### Citations:

Zbl 0628.65046
Full Text:
DOI

### References:

[1] | Glowinski R, Numerical analysis of variational inequalities (1981) |

[2] | Hackbysch W, Multi-grid methods and applications (1985) · doi:10.1007/978-3-662-02427-0 |

[3] | Hoppe R.H.W, SIAM J. Numer. Anal 24 (5) (1987) |

[4] | Kinderlehrer D, An introduction to variational inequalities and their applications (1980) · Zbl 0457.35001 |

[5] | Kirsten H, Optimization 16 pp 535– (1985) · doi:10.1080/02331938508843047 |

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