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

This book is devoted to the detailed description
of high-order hp-adaptive finite element schemes 
to be used in engineering simulations (in parti-
cular, the interesting case of automatic goal-
oriented hp-adaptivity is considered). The major
emphasis is on the algorithmic aspects of these
methods, with the goal of making easier their
practical implementation. 
  After a clear introduction to the theory of finite
elements and orthogonal polynomials, a complete
presentation of the most commonly used hierarchic 
master elements is given: very likely, this will
become a reference chapter for future practitioners.
The core of the book is in the two chapters on
higher-order approximation, in which the finite 
element discretization is completely described
and the important aspect concerned with the influence
of numerical quadrature is carefully analyzed.
  The last part of the book is related to mesh 
optimization and fully automatic h-, p- and hp-
adaptivity. The adaptive strategy, that is based
on automatic minimization of suitable interpolation 
errors, is carefully described, and its performances
are illustrated on several numerical examples. 
  Summing up. the book is well-written, and the 
overall structure clear and well-explained. I think
that it surely will meet the interest of applied
mathematicians, engineers and practitioners.

Alberto Valli, Universita degli studi di Trento, Trento, Italy.