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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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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 23 August 2019

FUNDAMENTAL CONCEPTS IN ONE DIMENSION

FUNDAMENTAL CONCEPTS IN ONE DIMENSION

Chapter:
(p.16) 2 FUNDAMENTAL CONCEPTS IN ONE DIMENSION
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/9780198528692.003.0002

This chapter discusses the fundamental concepts that are further developed in the remainder of the book, in the context of a one-dimensional formulation. In doing so, the principles and underlying theory behind the construction of the spectral/hp element method are illustrated. Topics covered include method of weighted residuals, Galerkin formulation, one-dimensional expansion bases, elemental operations, error estimates, and implementation of a one-dimensional spectral/hp element. The chapter ends with exercises aimed at developing a one-dimensional spectral element solver.

Keywords:   spectral/hp element method, weighted residuals, Galerkin formulation, one-dimensional expansion bases, numerical integration, differentiation, error estimates

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