Jan S. Hesthaven, Tim Warburton (auth.)9780387720654, 0387720650, 0387720677
This book discusses a family of computational methods, known as discontinuous Galerkin methods, for solving partial differential equations. While these methods have been known since the early 1970s, they have experienced an almost explosive growth interest during the last ten to fifteen years, leading both to substantial theoretical developments and the application of these methods to a broad range of problems.
These methods are different in nature from standard methods such as finite element or finite difference methods, often presenting a challenge in the transition from theoretical developments to actual implementations and applications.
This book is aimed at graduate level classes in applied and computational mathematics. The combination of an in depth discussion of the fundamental properties of the discontinuous Galerkin computational methods with the availability of extensive software allows students to gain first hand experience from the beginning without eliminating theoretical insight.
Jan S. Hesthaven is a professor of Applied Mathematics at Brown University.
Tim Warburton is an assistant professor of Applied and Computational Mathematics at Rice University.
Table of contents :
Front Matter….Pages I-XIV
Introduction….Pages 1-17
The key ideas….Pages 19-41
Making it work in one dimension….Pages 43-74
Insight through theory….Pages 75-113
Nonlinear problems….Pages 115-168
Beyond one dimension….Pages 169-241
Higher-order equations….Pages 243-330
Spectral properties of discontinuous Galerkin operators….Pages 331-372
Curvilinear elements and nonconforming discretizations….Pages 373-406
Into the third dimension….Pages 407-443
Back Matter….Pages 445-501
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