Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

Request Permissions   Purchase Content 
 

 

Commuting diagrams for the TNT elements on cubes


Authors: Bernardo Cockburn and Weifeng Qiu
Journal: Math. Comp. 83 (2014), 603-633
MSC (2010): Primary 65N30, 65L12
Published electronically: June 18, 2013
MathSciNet review: 3143686
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We present commuting diagrams for the de Rham complex for new elements defined on cubes which use tensor product spaces. The distinctive feature of these elements is that, in sharp contrast with previously known results, they have the TiNiest spaces containing Tensor product spaces of polynomials of degree $ k$, hence their acronym TNT. In fact, the local spaces of the TNT elements differ from the standard tensor product spaces by spaces whose dimension is a small number independent of the degree $ k$. Such a number is 7 (the number of vertices of the cube minus one) for the space associated with the divergence operator, 18 (the number of faces of the cube times the number of vertices of a face minus one) for the space associated with the curl operator, and 12 (the number of edges of the cube times the number of vertices of an edge minus one) for the space associated with the gradient operator.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65N30, 65L12

Retrieve articles in all journals with MSC (2010): 65N30, 65L12


Additional Information

Bernardo Cockburn
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: cockburn@math.umn.edu

Weifeng Qiu
Affiliation: Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, Minnesota 55455
Email: qiuxa001@ima.umn.edu, qiuw78@gmail.com

DOI: https://doi.org/10.1090/S0025-5718-2013-02729-9
Keywords: Commuting diagrams, cubic element, tensor product spaces
Received by editor(s): July 12, 2011
Received by editor(s) in revised form: March 5, 2012, March 30, 2012, and June 21, 2012
Published electronically: June 18, 2013
Additional Notes: The first author was partially supported by the National Science Foundation (Grant DMS-0712955) and by the Minnesota Supercomputing Institute.
The second author gratefully acknowledges the collaboration opportunities provided by IMA (Minneapolis) during their 2010–2012 program. \indent Corresponding author: Weifeng Qiu
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.