A Comparison of High Order Interpolation Nodes for the Pyramid
Author
Chan, Jesse; Warburton, T.
Date
2015Abstract
The use of pyramid elements is crucial to the construction of efficient hex-dominant meshes [M. Bergot, G. Cohen, and M. Duruflé, J. Sci. Comput., 42 (2010), pp. 345--381]. For conforming nodal finite element methods with mixed element types, it is advantageous for nodal distributions on the faces of the pyramid to match those on the faces and edges of hexahedra and tetrahedra. We adapt existing procedures for constructing optimized tetrahedral nodal sets for high order interpolation to the pyramid with constrained face nodes, including two generalizations of the explicit warp and blend construction of nodes on the tetrahedron [T. Warburton, J. Engrg. Math., 56 (2006), pp. 247--262]. Comparisons between nodal sets show that the lowest Lebesgue constants are given by warp and blend nodes for order $N\leq 7$ and Fekete nodes for $N>7$, though numerical experiments show little variation in the conditioning and accuracy of all surveyed nonequidistant points.
Citation
Published Version
Type
Journal article
Publisher
Citable link to this page
https://hdl.handle.net/1911/94789Rights
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Metadata
Show full item recordCollections
- CAAM Publications [77]
- Faculty Publications [5504]