## Frontiers in Numerical Analysis: Durham 2002James Blowey, Alan Craig, Tony Shardlow The Tenth LMS-EPSRC Numerical Analysis Summer School was held at the University of Durham, UK, from the 7th to the 19th of July 2002. This was the second of these schools to be held in Durham, having previously been hosted by the University of Lancaster and the University of Leicester. The purpose of the summer school was to present high quality instructional courses on topics at the forefront of numerical analysis research to postgraduate students. The speakers were Franco Brezzi, Gerd Dziuk, Nick Gould, Ernst Hairer, Tom Hou and Volker Mehrmann. This volume presents written contributions from all six speakers which are more comprehensive versions of the high quality lecture notes which were distributed to participants during the meeting. At the time of writing it is now more than two years since we first contacted the guest speakers and during that period they have given significant portions of their time to making the summer school, and this volume, a success. We would like to thank all six of them for the care which they took in the preparation and delivery of their material. |

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### Contents

III | 1 |

V | 2 |

VI | 3 |

VII | 6 |

VIII | 8 |

IX | 9 |

X | 11 |

XI | 14 |

LXXXVI | 160 |

LXXXVII | 161 |

LXXXVIII | 163 |

LXXXIX | 165 |

XC | 167 |

XCII | 175 |

XCIII | 176 |

XCIV | 177 |

XII | 15 |

XIII | 17 |

XV | 19 |

XVI | 25 |

XVII | 36 |

XVIII | 44 |

XIX | 52 |

XX | 61 |

XXI | 63 |

XXIII | 67 |

XXIV | 68 |

XXV | 69 |

XXVI | 71 |

XXVIII | 75 |

XXIX | 80 |

XXXI | 84 |

XXXII | 85 |

XXXIII | 86 |

XXXIV | 87 |

XXXV | 89 |

XXXVI | 90 |

XXXVIII | 91 |

XXXIX | 93 |

XL | 94 |

XLI | 100 |

XLII | 102 |

XLIII | 104 |

XLIV | 106 |

XLV | 109 |

XLVI | 111 |

XLVII | 112 |

XLVIII | 113 |

XLIX | 114 |

L | 115 |

LII | 116 |

LIII | 117 |

LV | 119 |

LVI | 122 |

LVII | 123 |

LVIII | 124 |

LIX | 126 |

LX | 127 |

LXI | 128 |

LXII | 130 |

LXV | 131 |

LXVI | 133 |

LXVII | 136 |

LXVIII | 137 |

LXIX | 141 |

LXX | 143 |

LXXI | 144 |

LXXIII | 146 |

LXXV | 147 |

LXXVI | 148 |

LXXVII | 149 |

LXXVIII | 150 |

LXXX | 151 |

LXXXI | 152 |

LXXXII | 153 |

LXXXIV | 155 |

LXXXV | 156 |

XCV | 178 |

XCVII | 179 |

XCIX | 199 |

C | 200 |

CI | 202 |

CII | 203 |

CIII | 206 |

CV | 208 |

CVI | 209 |

CVII | 210 |

CVIII | 211 |

CIX | 217 |

CX | 218 |

CXII | 220 |

CXIII | 222 |

CXIV | 226 |

CXVI | 228 |

CXVII | 230 |

CXVIII | 231 |

CXIX | 232 |

CXXI | 234 |

CXXIII | 235 |

CXXIV | 236 |

CXXV | 238 |

CXXVI | 241 |

CXXVIII | 243 |

CXXX | 247 |

CXXXI | 254 |

CXXXII | 256 |

CXXXIII | 259 |

CXXXIV | 264 |

CXXXV | 267 |

CXXXVI | 268 |

CXXXVII | 270 |

CXXXVIII | 272 |

CXXXIX | 275 |

CXL | 276 |

CXLI | 278 |

CXLII | 287 |

CXLIII | 289 |

CXLIV | 290 |

CXLV | 295 |

CXLVI | 297 |

CXLVII | 303 |

CXLIX | 306 |

CLI | 310 |

CLII | 311 |

CLIII | 312 |

CLIV | 313 |

CLV | 315 |

CLVI | 318 |

CLVII | 321 |

CLVIII | 326 |

CLX | 331 |

CLXI | 336 |

CLXII | 340 |

CLXIII | 344 |

CLXIV | 346 |

CLXV | 347 |

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Frontiers in Numerical Analysis: Durham 2002 James Blowey,Alan Craig,Tony Shardlow Limited preview - 2012 |

### Common terms and phrases

algebraic algorithm analysis anisotropic apply approximation assume assumptions base functions boundary coarse grid coefficients compute consider constraints convergence defined denote differential equations discrete eigenvalue problems eigenvectors equivalent error estimate Euler example finite element method given global gradient Hamiltonian systems Hence Hessian homogenization implies integration invariant subspace iteration Lagrange multipliers Lemma level set linear linesearch linesearch methods Lipschitz continuous Math Mathematics Matlab matrix mean curvature mean curvature flow merit function minimizer multiscale finite element multiscale method multistep methods nonlinear nonsingular norms numerical methods numerical solution obtain optimal control orthogonal oscillatory p-reversible positive definite positive semidefinite Programming Proof of Theorem quadratic Quasi-Newton Methods result Riccati Riccati equation Runge-Kutta methods satisfies scheme Schur form Section SIAM solve space SQP methods step structure subproblem symmetric symplectic Theorem 3.1 theory tion trust-region methods unique solution upscaling vector viscosity solution zero

### Popular passages

Page 300 - Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods.