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**Multigrid algorithms for the solution of linear complementarity problems arising from free boundary problems.**
*(English)*
Zbl 0542.65060

The multigrid FAS algorithm of the first author is adapted to handle the complementarity problems arising from finite difference approximations of elliptic variational inequalities of the obstacle type. This is accomplished by the use of projected relaxation for smoothing and by a suitable modification of the correction problem taking into account the constraints. It is shown by numerical examples that for large problems the method is significantly faster than previous methods. The observed computational time is proportional to the number of points on the finest grid. Several modifications of the method are considered, which further improve its efficiency.

Reviewer: J.Mandel

### MSC:

65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |

65K10 | Numerical optimization and variational techniques |

49J40 | Variational inequalities |

35R35 | Free boundary problems for PDEs |

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |

35J65 | Nonlinear boundary value problems for linear elliptic equations |