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Spectral/hp Element Methods for Computational Fluid Dynamics$
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George Karniadakis and Spencer Sherwin

Print publication date: 2005

Print ISBN-13: 9780198528692

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198528692.001.0001

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MULTI-DIMENSIONAL EXPANSION BASES

MULTI-DIMENSIONAL EXPANSION BASES

Chapter:
(p.81) 3 MULTI-DIMENSIONAL EXPANSION BASES
Source:
Spectral/hp Element Methods for Computational Fluid Dynamics
Author(s):

George Em Karniadakis (Contributor Webpage)

Spencer J. Sherwin

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198528692.003.0003

This chapter considers the extension of the one-dimensional formulation to two and three dimensions by the development of expansion bases in standard regions such as triangles or rectangles in two dimensions, and tetrahedrons, prisms, pyramids, and hexahedrons in three dimensions. The construction of these bases uses a unified approach for the development of computationally efficient expansions. The modal basis is formulated as solutions to a generalized Sturm-Liouville problem. Optimal nodal points, the so-called Fekete points, the electrostatic points on a simplex, and related approximation results, are also presented. The exercises at the end of the chapter target construction of multi-dimensional elemental matrices.

Keywords:   tensor product expansions, modal expansions, non-tensorial nodal expansions, Sturm-Liouville problem, Fekete points, electrostatic points

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