EAN: 9783642229794

MATHEMATICAL ASPECTS OF DISCONTINUOUS GALERKIN ...

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.

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