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research article

Isogeometric discrete differential forms in three dimensions

Buffa, Annalisa  
•
Rivas, J.
•
Sangalli, G.
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2011
SIAM Journal on Numerical Analysis

The concept of isogeometric analysis (IGA) was first applied to the approximation of Maxwell equations in [A. Buffa, G. Sangalli, and R. Vázquez, Comput. Methods Appl. Mech. Engrg., 199 (2010), pp. 1143-1152]. The method is based on the construction of suitable B-spline spaces such that they verify a De Rham diagram. Its main advantages are that the geometry is described exactly with few elements, and the computed solutions are smoother than those provided by finite elements. In this paper we develop the theoretical background to the approximation of vector fields in IGA. The key point of our analysis is the definition of suitable projectors that render the diagram commutative. The theory is then applied to the numerical approximation of Maxwell source problems and eigenproblems, and numerical results showing the good behavior of the scheme are also presented. Copyright © 2011 Society for Industrial and Applied Mathematics.

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Type
research article
DOI
10.1137/100786708
Author(s)
Buffa, Annalisa  
Rivas, J.
Sangalli, G.
Vázquez Hernández, Rafael  
Date Issued

2011

Published in
SIAM Journal on Numerical Analysis
Volume

49

Issue

2

Start page

818

End page

844

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
MNS  
Available on Infoscience
April 3, 2017
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/136316
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