Incompressible flow and the finite element method

It was with a rare pleasure that I read these books and I have already used them many times as handbooks. As the title indicates, the books are about incompressible flow and finite elements. However, it may be worth pointing out that the books are useful for a broader numerical methods audience. In parts of the books finite volume and finite difference discretizations are discussed and compared with finite elements. This is done in a way that should increase better understanding of these methods and could help in transferring knowledge between the different communities. Moreover, readers interested in compressible flows would benefit as well, since modelling of incompressible flows has automatically to address many aspects of compressible flow modelling. Throughout the books the authors reveal an in-depth understanding of the subject as well as an awareness of what has been done so far. This is not surprising, as they are very well known and respected among the finite element method community. What is most pleasing is that some subjects that are frequently explained by others in a somewhat unclear way, or avoided altogether, are specifically targeted and thoroughly explained in these books. They mention, for example, issues of consistent mass matrix and lumped matrix, or null spaces and choice of elements for pressure and velocity interpolations. There are many more items worth detailed reading. The discussion about ‘wiggles’, which expands on the frequently cited publication by P. M. Gresho and R. L. Lee ‘Don’t suppress the wiggles—they’re telling you something’, is especially educational and entertaining. In fact, the whole book is entertaining. The style is very informal and (in my opinion) enjoyable. There are jokes in the text and you will be urged to wake up if you do not perceive that the authors are in favour of Gallerkin methods. Of course, readers with a different sense of humour may find the style irritating. Nevertheless, the text is always very clear. In fact, many difficult issues are explained in a simple way, which in itself is a difficult thing to do. The books address most aspects of modelling incompressible, isothermal, laminar flow by the finite element method. In the first volume the advection–diffusion equation is studied as a vehicle to introduce an explanation for the methodologies provided later to solve the Navier– Stokes equations. The books are correctly addressed to readers with some background in CFD and FEM. For complete beginners there is a good list (with brief comments) of recommended textbooks, which should provide a start. The books are particularly suitable for PhD students with projects in relevant subjects. I found that to benefit most from the explanations, it is best to read it for the first time in sequential order. The books should also be very useful to more ‘seasoned’ researchers. They provide a very comprehensive overview of the state-of-the-art. The references are very much up-to-date and well chosen. With a large number of papers being published in this field these books can save the reader time, since the key information is well selected, analysed and presented by the authors. The major trends of research are courteously commented on with more than average frankness. This may be of interest even to readers not sharing the authors’ preferences. As yet, on every attempt, I have been able to find in these books detailed information I needed. The paperback price of £80 for two volumes is reasonable. Only infrequently are such good textbooks published and therefore I would also recommend them as a good buy for research libraries. If the reader finds criticisms, these experienced authors have most probably apologized for them in the introduction. There seems to be every eventuality covered. There is also a promise to write a third volume to complete the picture.