hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes. 1st ed. 2017

種類:

電子ブック

責任表示:

by Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Cangiani, Andrea.
• Dong, Zhaonan.
• Georgoulis, Emmanuil H.
• Houston, Paul.
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematics ;

ISBN:

9783319676739 [3319676733]    

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 elemen

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