Mathematical Aspects of Discontinuous Galerkin MethodsSpringer Science & Business Media, 03.11.2011 - 384 Seiten This book introduces the basic ideas to build discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. The presentation 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 exploited 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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Mathematical Aspects of Discontinuous Galerkin Methods Daniele Antonio Di Pietro,Alexandre Ern Keine Leseprobe verfügbar - 2011 |
Mathematical Aspects of Discontinuous Galerkin Methods Daniele Antonio Di Pietro,Alexandre Ern Keine Leseprobe verfügbar - 2011 |
Häufige Begriffe und Wortgruppen
admissible mesh sequence advection-reaction advective approximation error assume assumption bound boundary conditions boundary field boundedness broken polynomial space Cauchy–Schwarz inequality CFL condition Cockburn consider context convergence analysis convergence rate defined Definition denotes derive dG approximation dG methods diffusive flux Dirichlet boundary conditions discrete bilinear form discrete coercivity discrete gradient discrete problem discrete solution discrete stability discrete trace inequality equations error estimates exact solution Fe F Fe F# Fe3F Fe3FT finite element finite element methods formulation Friedrichs function Galerkin methods Hölder's inequality independent of h infer interface jumps linear mesh element mesh faces Moreover norm numerical flux observe obtain operator PDEs penalty parameter Poincaré inequality Poisson problem polynomial degree real number Remark right-hand side Sect seminorm SIP bilinear form Sobolev spaces solve space semidiscrete Theorem triangle inequality velocity well-posed well-posedness yields