Titlebook: Nodal Discontinuous Galerkin Methods; Algorithms, Analysis Jan S. Hesthaven,Tim Warburton Textbook 2008 Springer-Verlag New York 2008 3D.An

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Beyond one dimension,nal problems. In this chapter we consider in more detail the extension to multidimensional problems and the challenges introduced by this. We will quickly realize that what may have seemed unnecessarily complicated in the one-dimensional case now enables us to expand the formulation to multiple dimensions with only minor changes.

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Into the third dimension,ction of nodal sets for the triangle and an orthonormal polynomial basis that we used as a reference basis for interpolation, differentiation, and the computation of inner products. In this chapter we will go further and consider the additional details required to extend this approach to three-dimensional domains.

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978-1-4419-2463-6Springer-Verlag New York 2008

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Introduction,thods for doing so. Among these are the widely used finite difference, finite element, and finite volume methods, which are all techniques used to derive discrete representations of the spatial derivative operators. If one also needs to advance the equations in time, there is likewise a wide variety

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The key ideas,oundary ∂Ω and assume that this domain is well approximated by the computational domain Ω.. This is a space filling triangulation composed of a collection of . geometry-conforming nonoverlapping elements, D.. The shape of these elements can be arbitrary although we will mostly consider cases where t

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