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

This text provides a timely and balanced introduction to the very
active research area of hp-adaptive methods for the solution of
partial differential equations. Emphasis is placed on conforming
finite element methods employing hierarchial p-order basis functions 
with applications to adaptive solution of problems in electromagnetics,
elastodynamics, acoustics etc

The text stands out by not only providing an coherent overview of the 
central mathematical techniques and formulations for approximating PDE's, 
but also by paying attention to many practical aspects of implementations. 
The detailed overview of element types and quadrature rules provide a 
valuable reference, while the discussion of suitable data structures 
and efficient linear solvers provide an excellent introductions to key 
aspects, often neglected, of this class of methods. 
The detailed overviews, supported by numerous examples, of
p-type finite element methods and various hp-adaptive strategies present 
delightful introduction to these rapidly expanding research areas.

The text, written by accomplished researcher, is broad and written
at a level that will appeal to graduate students and researchers
entering the research area. The many details on implementation and
practical aspects and suggestions will be invaluable in this case. 
However, the text will likewise be valuable for specialists as a place
to seek reference information.

Jan Hesthaven, Brown University, Providence, RI