Theory and Numerics of Differential Equations: Durham 2000James Blowey, John P. Coleman, Alan W. Craig The Ninth EPSRC Numerical Analysis Summer School was held at the Uni versity of Durharn, UK, from the 10th to the 21st of July 2000. This was the first of these schools to be held in Durharn, having previously been hosted, initially by the University of Lancaster and latterly by the University of Leicester. The purpose of the summer school was to present high quality in structional courses on topics at the forefront of numerical analysis research to postgraduate students. Eminent figures in numerical analysis presented lectures and provided high quality lecture notes. At the time of writing it is now more than two years since we first con tacted the guest speakers and during that period they have given significant portions of their time to making the summer school, and this volume, a suc cess. We would like to thank all six of them for the care which they took in the preparation and delivery of their lectures. The speakers were Christine Bernardi, Petter Bj0rstad, Carsten Carstensen, Peter Kloeden, Ralf Kornhu ber and Anders Szepessy. This volume presents written contributions from five of the six speakers. In all cases except one, these contributions are more comprehensive versions of the lecture not es which were distributed to participants during the meeting. Peter Kloeden's contribution is intended to be complementary to his lecture course and numerous references are given therein to sources of the lecture material. |
Contents
| 1 | |
Extension to more Complex Geometries | 36 |
References | 53 |
Function Spaces | 66 |
Typical Information from Infimizing Sequences | 75 |
Energy Minimization Rates | 85 |
Young Measure Relaxation | 100 |
Equivalence | 107 |
Stratonovich Stochastic Calculus | 137 |
Linear Vector SDEs | 147 |
Commutative and Coloured Noise | 157 |
Weak Numerical Schemes | 170 |
References | 176 |
Smooth Nonlinear Problems | 190 |
Piecewise Smooth Semilinear Problems | 208 |
References | 225 |
Numerical Algorithms | 116 |
Summary | 122 |
Stochastic Differential Equations | 128 |
Adaptive Numerics for Differential Equations | 247 |
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Theory and Numerics of Differential Equations James Blowey,John P. Coleman,Alan W. Craig No preview available - 2014 |
Common terms and phrases
2-dimensional Algorithm approximation bounded calculus commutative noise computed conservation laws constant convergence rates convex defined Delta denotes derive dimension discrete problem domain element method error estimate estimate holds Example finite element formula function global grid Hence inequality infimizing sequence initial integral Ito SDE Legendre Lemma linear lower semicontinuous Maday Math matrix measure valued solution mesh microstructure minimization problem monotone multigrid multigrid method Navier-Stokes equations nested iteration Newton multigrid nonlinear nops nops op 1,b norm numerical analysis optimal parameters partial differential polynomial posteriori Proof Proposition Remark routine stochastic satisfies scalar Section smooth Sobolev Sobolev spaces soln solve space spectral spectral element method spectral methods stochastic differential equations Stratonovich subspace Theorem tn+1 variables variational vector Wiener process X₁ Young measure