Mathematical Aspects of Discontinuous Galerkin Methods [electronic resource] / by Daniele Antonio Di Pietro, Alexandre Ern.
Contributor(s): Ern, Alexandre [author.] | SpringerLink (Online service)Material type: TextSeries: Mathématiques et Applications: 69Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012Description: XVII, 384 p. 34 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783642229800Subject(s): Mathematics | Computer mathematics | Numerical analysis | Applied mathematics | Engineering mathematics | Mathematics | Numerical Analysis | Computational Mathematics and Numerical Analysis | Appl.Mathematics/Computational Methods of EngineeringAdditional physical formats: Printed edition:: No titleDDC classification: 518 LOC classification: QA297-299.4Online resources: Click here to access online
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Basic concepts -- Steady advection-reaction -- Unsteady first-order PDEs -- PDEs with diffusion -- Additional topics on pure diffusion -- Incompressible flows -- Friedhrichs' Systems -- Implementation.
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.