New book, Nodal DG-FEM: Algorithms, Analysis and Applications

Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Jan S Hesthaven and Tim Warburton
Springer Texts in Applied Mathematics 54, Springer Verlag, New York.
ISBN: 978-0-387-72065-4
http://www.springer.com/west/home/math/cse?SGWID=4-10045-22-173736528-0

This book offers an introduction to the key ideas, basic analysis, and
efficient implementation of discontinuous Galerkin finite element
methods (DG-FEM) for the solution of partial differential
equations. It is the first text on DG-FEM that covers both theoretical
developments, practical implementation aspects, and general
applications, and it is suitable both as a textbook and for self study
with exercises included at the end of most chapters.

The text covers all main theoretical results, including an overview of
relevant results from approximation theory, stability and convergence
theory for numerical partial differential equations, and orthogonal
polynomials. The book describes in more detail DG-FEM discretizations
for a number of classic systems of time dependent partial differential
equations: Maxwell's equations, Euler's equations, the incompressible
Navier-Stokes equations as well as the static Poisson and Helmholtz
equations. The formulations and associated analysis are provided in
detail for one- and two- dimensions computations on general finite
element meshes with high-order elements, both in terms of analysis and
through complete algroithms in embedded Matlab software. The essential
details and Matlab functions for three-dimensional computations are
included and briefly discussed. The three appendices contain an
overview of orthogonal polynomials and associated library routines
used throughout the text, a brief introduction to grid generation, and
an overview of the included Matlab software.

The embedded software as well as many other related resources are all
freely available at the associated webpage: http://www.nudg.org.
Received on Thu Jan 3 07:55:00 2008