HIGHER-ORDER FINITE ELEMENT METHODS
P. Solin, K. Segeth, I. Dolezel

  This monograph presents in 400 pages the theory and application of
higher-orderfinite element methods in H^1, H(curl) and H(div) spaces,
starting from the  1-dimensional case (with nonhomogenous Dirichlet
conditions) and including a database of master elements of arbitrary
order on the most commonly used reference domains in 2D and 3D. The
approach is consistently rigorous and systematic, and special care is
taken for the proper implementation of higher-order numerical quadrature
in 2 and 3 spatial dimensions, in view of the non-uniqueness of the
Gaussian weights and points.
  This work also gives an overview of the contemporary direct and
iterative methods for the solution of large systems of linear equations,
and concludes with an approach to goal-oriented adaptivity and automatic
mesh optimization and h-, p- and hp-adaptivity based on the concept of
reference solutions.
  Through a judicious use of mathematical language, this book has been
designed to be readable by engineers and applied scientists as well
as mathematicians. Only a modest knowledge of (standard) FEMs is
presumed from the reader. Actually, the book is selfcontained to a high
extent. For instance, it provides a working introduction to orthogonal
poynomials and to numerical quadrature. The book is completed by an
author index, a detailed subject index and a valauble, extensive list of
references (up to 2002).
  Moreover, the overall structure of this  comprehensive monograph is very
transparant and the style of presentation of the material has an
expository nature. These features make the book suitable both as a
textbook for selfstudy for researchers, as a reference book and as
supporting material for (post)graduate courses in advanced FEMs. There
is no doubt that this new monograph on recent topics of finite element
theory and applications will be welcomed by the broad community of
finite element researchers and lecturers, both by the practioners and by
the numerical functional analysists.

Roger Van Keer, University of Gent, Belgium.