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Mathematics - Computational Science & Engineering | Mathematical Aspects of Discontinuous Galerkin Methods

Mathematical Aspects of Discontinuous Galerkin Methods

Di Pietro, Daniele Antonio, Ern, Alexandre

2012, XVII, 384p.

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  • Understanding the mathematical foundations helps the reader design methods for new applications 
  • Bridging the gap between finite volumes, finite elements, and discontinuous Galerkin methods provides new insight on numerical methods
  • The mathematical setting for the continuous model is a key to successful approximation methods
This book introduces the basic ideas for building discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. It is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite-element and finite-volume viewpoints are utilized to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.

Content Level » Research

Keywords » Discontinuous Galerkin methods - First-order PDEs - Friedrichs' systems - Incompressible Navier-Stokes equations - Second-order PDEs

Related subjects » Computational Intelligence and Complexity - Computational Science & Engineering

Table of contents / Sample pages 

Basic concepts.- Steady advection-reaction.- Unsteady first-order PDEs.- PDEs with diffusion.- Additional topics on pure diffusion.- Incompressible flows.- Friedhrichs' Systems.- Implementation.

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