Frontiers of Numerical Analysis

The Eleventh LMS-EPSRC Computational Mathematics and Scientific Com- puting Summer School was held at the University of Durham, UK, from the 4th of July to the 9th of July 2004. This was the third of these schools to be held in Durham, having previously been hosted by the University of Lan- caster and the University of Leicester. The purpose of the summer school was to present high quality instructional courses on topics at the forefront of computational mathematics and scientific computing research to postgradu- ate students. The main speakers were Emmanuel Candes, Markus Melenk, Joe Monaghan and Alex Schweitzer.

This book contains detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own and graduates in mathematical sciences.

Analysis of large deformation, rigid body movement and strain or stress for discontinuous materials is often required for project designs and plans in the fields of engineering and disaster prevention. Many numerical simulation and analysis methods have been developed for the requirement from science and technology people since 1970s.