Nodal discontinuous galerkin methods : algorithms, analysis, and applications
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Bibliographic Information
Nodal discontinuous galerkin methods : algorithms, analysis, and applications
（Texts in applied mathematics, 54）
Springer, c2008
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Includes bibliographical references and indexes
Description and Table of Contents
Description
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 covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE's, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE's: Maxwell's equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.
Table of Contents
The key ideas.- Making it work in one dimension.- Insight through theory.- Nonlinear problems.- Beyond one dimension.- Higher-order equations.- Spectral properties of discontinuous Galerkin operators.- Curvilinear elements and nonconforming discretizations.- Into the third dimension.
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