Mark Ainsworth - Böcker

An up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on aposteriori error estimation for finite element approximation inmechanics and mathematics. It emphasizes methods for ellipticboundary value problems and includes applications to incompressibleflow and nonlinear problems. Recent years have seen an explosion in the study of a posteriorierror estimators due to their remarkable influence on improvingboth accuracy and reliability in scientific computing. In an effortto provide an accessible source, the authors have sought to presentkey ideas and common principles on a sound mathematicalfooting. Topics covered in this timely reference include:* Implicit and explicit a posteriori error estimators* Recovery-based error estimators* Estimators, indicators, and hierarchic bases* The equilibrated residual method* Methodology for the comparison of estimators* Estimation of errors in quantities of interest A Posteriori Error Estimation in Finite Element Analysis is a lucidand convenient resource for researchers in almost any field offinite element methods, and for applied mathematicians andengineers who have an interest in error estimation and/or finiteelements.

This volume consists ofsurvey articles on current topics in computational wave prop­ agation and inverse problems, written by leading experts in their respective fields. The idea to compile such a volume arose in conjunction with the LMS Durham Symposium on Computational Methods for Wave Propagation in Direct Scattering held at the University of Durham from 15th-25th July 2002, which we jointly or­ ganised. The meeting, attended by 70 participants from the UK and overseas, was structured around a number of short, three lecture, survey courses on a range of top­ ics on computational wave propagation and inverse problems beginning at the level of a graduate student. We were delighted to secure the participation of distinguished international researchers to present these lectures. We felt that it would be valuable to record this material for the benefit of a wider audience, and the idea was hatched that the individual lecturers should be invited to contribute a survey article. Fortunately, many of the speakers not only agreed to undertake this arduous task, but produced what we hope you will agree are the high quality contributions found in this volume. Finally, it is a pleasure to thank the Engineering and Physical Sciences Research Council of Great Britain and the London Mathematical Society for providing the generous support that allowed the meeting to take place. Mark Ainsworth Glasgow, 2003 Penny Davies Dugald Duncan Paul Martin Bryan Rynne Contents New Results on Absorbing Layers and Radiation Boundary Conditions Thomas Hagstrom .

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.