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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Discontinuous Galerkin Methods for Linear Problems: An Introduction
verfasst von : Emmanuil H. Georgoulis
Erschienen in: Approximation Algorithms for Complex Systems
Verlag: Springer Berlin Heidelberg
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Discontinuous Galerkin (dG) methods for the numerical solution of partial differential equations (PDE) have enjoyed substantial development in re- cent years. Possible reasons for this are the flexibility in local approximation they offer, together with their good stability properties when approximating convection- dominated problems. Owing to their interpretation both as Galerkin projections onto suitable energy (native) spaces and, simultaneously, as high order versions of classical upwind finite volume schemes, they offer a range of attractive properties for the numerical solution of various classes of PDE problems where classical fi- nite element methods under-perform, or even fail. These notes aim to be a gentle introduction to the subject.