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＜電子ブック＞
hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes / by Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
本文言語	英語
大きさ	VIII, 131 p. 32 illus., 1 illus. in color : online resource
著者標目	*Cangiani, Andrea author Dong, Zhaonan author Georgoulis, Emmanuil H author Houston, Paul author SpringerLink (Online service)
件　名	LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Mathematical physics FREE:Computational Mathematics and Numerical Analysis FREE:Mathematics of Computing FREE:Theoretical, Mathematical and Computational Physics
一般注記	1 Introduction -- 2 Introduction to Discontinuous Galerkin Methods -- 3 hp–Inverse and Approximation Estimates -- 4 DGFEMs for Pure Diffusion Problems -- 5 DGFEMs for second–order PDEs of mixed–type -- 6 Implementation Aspects -- 7 Adaptive Mesh Refinement -- 8 Summary and Outlook -- References Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios. HTTP:URL=https://doi.org/10.1007/978-3-319-67673-9

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