Mathematical aspects of discontinuous Galerkin methods / Daniele Antonio Di Pietro, Alexandre Ern

Auteur: Di Pietro, Daniele Antonio (1979-) - AuteurCo-auteur: Ern, Alexandre (1967-) - AuteurType de document: MonographieCollection: Mathématiques et applications ; 69Langue: anglaisPays: AllemagneÉditeur: Berlin : Springer-Verlag, 2012Description: 1 vol. (XVII-384 p.) : fig. ; 24 cm ISBN: 9783642229794 ; br. Résumé: 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. (Source : 4ème de couverture).Bibliographie: Bibliogr. p. 355-373. Index. Sujets MSC: 65N30 Numerical analysis -- Partial differential equations, boundary value problems -- Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65M60 Numerical analysis -- Partial differential equations, initial value and time-dependent initial-boundary value problems -- Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
76M10 Fluid mechanics -- Basic methods in fluid mechanics -- Finite element methods
65-02 Numerical analysis -- Research exposition (monographs, survey articles)
76R50 Fluid mechanics -- Diffusion and convection -- Diffusion
76M12 Fluid mechanics -- Basic methods in fluid mechanics -- Finite volume methods
En-ligne: Springerlink
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Bibliogr. p. 355-373. Index

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. (Source : 4ème de couverture)

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