1228 BOOK REVIEWS

ACCURACY ESTIMATES AND ADAPrIVP RTEINEMENTS IN FINITF PI FMPNT COMPUTATIONS, I. BabuSka, 0. C. Zienkiewicz, J. Gago, E. R. deA. Oliviera (eds.). Wiley, Chichester, 1986. No. of pages: 408. Price: &49.50/$87.15. ISBN 0- 471 908622.

The use of a-posteriori error estimation and adaptive refinement is becoming increasingly popular by finite element practitioners. Very roughly speaking, the aim of these techniques is to produce local estimates of the error in a computed finite element approximation and then to use this information to produce an optimal mesh (that is a mesh which uses the minimum number of degrees of freedom to produce an acceptably accurate solu- tion). The attractions of this approach are obvi- ous-first it is possible to guarantee the quality a t the solution as we remove the element of guesswork from mesh design, and secondly the solution is obtained with small computer storage require- ments and relatively short processing times.

This book is divided into two sections, ‘Basic Theory and Applications to Elliptic Problems’, and ‘Fluid Mechanics and Transient Problems’, although the section headings only roughly des-

cribe their contents. The 21 chapters are written by eminent researchers and engineers and are loosely based on keynote lectures given at a con- ference of the same name in Lisbon in June 1984. The contributors have been carefully chosen and the text may be regarded as a state-of-the-art pub- lication.

It must be said, to anyone who is interested in learning about these methods, that there are not yet any generally agreed techniques for even simple problems, but rather that a large number of avenues are being investigated. The publication of this book is timely, as an element of coherence is now beginning to creep in; it will be interesting to hear the keynote lectures of any similar conference a few ycars into the future. All in all this is one of the most exciting and fertile areas of finite element research at present, the area is important and, indeed, will become indispensable. This book is representative of all that.

ALAN CRAIG Department of Mathematical Sciences

Uniuersity of Durham