## 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

Appendix applications approximate problem approximate solutions approximation error assume assumptions bilinear form boundary bounded Brézis calculated Chapter closed convex computation condition conjugate gradient method consider constraints convex set deduce defined denote Dirichlet problem discretisation domain dual duality algorithm duality method Duvaut—Lions elasto—plastic equation equivalent example existence explicit scheme exterior approximations finite element method finite—dimensional finite—element fluid formulation function given Glowinski grad hence Hilbert space imation implies Initialisation inner product introduce l.lA Lagrangian Lemma linear Math nonlinear nonlinear programming norm notation number of iterations numerical analysis numerical results numerical solution obtain optimal over—relaxation parameter penalised problem 3.lA Proof Proposition prove regularisation relation Remark resp saddle point satisfied Section 5.2 sequence shown solution of P0 solution of problem solving strong convergence strongly sufficiently small symmetric Synopsis termination criterion Theorem time—dependent triangulation variational inequality VveK VveV weakly