hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes

Nonfiction, Science & Nature, Mathematics, Counting & Numeration, Computers, Database Management, Data Processing
Cover of the book hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes by Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston, Springer International Publishing
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Author: Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston ISBN: 9783319676739
Publisher: Springer International Publishing Publication: November 27, 2017
Imprint: Springer Language: English
Author: Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
ISBN: 9783319676739
Publisher: Springer International Publishing
Publication: November 27, 2017
Imprint: Springer
Language: English

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.  

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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.  

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