## Error Control and Adaptivity in Scientific ComputingHaydar Bulgak, Christoph Zenger One of the main ways by which we can understand complex processes is to create computerised numerical simulation models of them. Modern simulation tools are not used only by experts, however, and reliability has therefore become an important issue, meaning that it is not sufficient for a simulation package merely to print out some numbers, claiming them to be the desired results. An estimate of the associated error is also needed. The errors may derive from many sources: errors in the model, errors in discretization, rounding errors, etc. Unfortunately, this situation does not obtain for current packages and there is a great deal of room for improvement. Only if the error can be estimated is it possible to do something to reduce it. The contributions in this book cover many aspects of the subject, the main topics being error estimates and error control in numerical linear algebra algorithms (closely related to the concept of condition numbers), interval arithmetic and adaptivity for continuous models. |

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### Contents

Interval Arithmetic Tools for Range Approximation and Inclusion of Zeros | 1 |

A New Concept of Construction of Adaptive Calculation MOdels for Hyperbolic Problems | 23 |

Error Estimates in Linear Systems | 65 |

Error Estimates in Padé Approximation | 75 |

Error Estimates and Convergence Acceleration | 87 |

Pseudoeigenvalues Spectral Portrait of a Matrix and their Connections with Different Criteria of Stability | 95 |

Error Control for Adaptive Sparse Grids | 125 |

Orthogonal Matrix Decompositions in Systems and Control | 159 |

Model Reduction of LargeScale Systems and Control | 177 |

Adaptive Symplectic and Reversible Integrators | 191 |

Domain Decomposition Methods for Compressible Flows | 221 |

Error Control in Finite Element Computations An introduction to error estimation and the meshsize adaption | 247 |

Verified Solution of Large Linear and Nonlinear Systems | 279 |

The Accuracy of Numerical Models for Continuum Problems | 299 |

Domain Decomposition Methods for Elliptic Partial Differential Equations | 325 |

### Other editions - View all

Error Control and Adaptivity in Scientific Computing Haydar Bulgak,Christoph Zenger Limited preview - 1999 |

Error Control and Adaptivity in Scientific Computing Haydar Bulgak,Christoph Zenger Limited preview - 2012 |

Error Control and Adaptivity in Scientific Computing Haydar Bulgak,Christoph Zenger No preview available - 2012 |

### Common terms and phrases

adaptive algorithm applications asymptotically stable asymptotically stable matrix bound boundary conditions Brezinski Bulgak calculation model cells coefficients condition number consider constant constructed continuum convergence convergence acceleration corresponding defined denotes difference differential equations dimensional discrete asymptotically stable domain decomposition methods Dooren eigenvalues energy norm error analysis error control Euler equations example Figure finite element flow formula full potential equation function Gaussian elimination given Hamiltonian systems hierarchical inequality interface interpolation interval arithmetic iterative Kluwer Academic Publishers Lemma linear systems Lyapunov mathematical matrix equation mesh molecular dynamics multiple time stepping Navier-Stokes equations nonlinear numerical obtained operator optimal orthogonal parameters perturbation polynomial positive definite posteriori error estimate quadrature recursive refinement scheme Schur form Schwarz method sequence sequence transformation simulation singular value solution solving space sparse grid stability subspace substructure symmetric symplectic integrators Theorem tion transformation triangular variable step Verlet method Zenger zero

### Popular passages

Page 353 - Periaux, eds., First International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, 1988, pp.