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Mathematical Aspects of Discontinuous Galerkin Methods
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一本介绍 Discontinuous Galerkin method 的书,与其他方法的比较和关联,以及将其应用到一些具体的应用问题。 Author: D. A. Di Pietro and A. Ern publisher: Springer; Volume & Year:Volume 69, 2012 Preface: 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. |
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2014-07-07 11:05:57, 4.24 M
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