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hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes (Paperback, 1st ed. 2017)
Loot Price: R2,189
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hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes (Paperback, 1st ed. 2017)
Series: SpringerBriefs in Mathematics
Expected to ship within 10 - 15 working days
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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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