## Numerical Analysis of Variational InequalitiesNumerical Analysis of Variational Inequalities |

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### Contents

1 | |

Optimisation algorithms | 59 |

Numerical analysis of the problem of the elastoplastic torsion of a cylindrical bar | 117 |

Thermal control problems boundary unilateral problems and elliptic variational inequalities of order 4 | 249 |

Numerical analysis of the steady flow of a Bingham fluid in a cylindrical duct | 347 |

General methods for the approximation and solution of timedependent variational inequalities | 405 |

Further discussion of steadystate inequalities | 541 |

Further discussion of optimisation algorithms | 587 |

Further discussion of the numerical analysis of the elastoplastic torsion problem | 623 |

Further discussion of boundary unilateral problems and elliptic variational inequalities of order 4 Application to fluid mechanics | 653 |

Further discussion of the numeric alanalysis of the steady flow of a Bingham fluid in a cylindrica duct | 717 |

Further discussion of the numerical analysis of timedependent variatioal inequalities | 733 |

Bibliography of the Appendices | 767 |

### Common terms and phrases

algorithm applications approacimate approximate problem assume assumptions bilinear form boundary bounded calculated Chapter condition conjugate gradient method consider constraints convex set deduce defined denote Dirichlet problem diſ discretisation domain Duvaut-Lions dx Wv Eacample eacterior elasto-plastic equation equivalent example exterior approximations finite element method finite-dimensional finite-element fluid formulation fu dx function given Glowinski grad gradient hence Hilbert space Hö(Q imation implies Initialisation inner product Lagrangian Lemma linear Math minimisation nonlinear norm notation number of iterations numerical analysis numerical solution obtain optimal over-relaxation parameter Proof Proposition prove regularisation Remark resp saddle point satisfies scheme Section H sequence shown ſº solving strongly sufficiently small symmetric termination criterion Theorem time-dependent triangulation unique variational inequality weakly