The problem of constructing hierarchic bases for finite element discretization of the spaces H 1, H (curl ), H (div ) and L 2 on tetrahedral elements is addressed. A simple and efficient approach to ensuring conformity of the approximations across element interfaces is described. Hierarchic bases of arbitrary polynomial order are presented. It is shown how these may be used to construct finite element approximations of arbitrary, non‐uniform, local order approximation on unstructured meshes of curvilinear tetrahedral elements.
%0 Journal Article
%1 noauthororeditor
%A Ainsworth, Mark
%A Coyle, Joe
%D 2003
%J International Journal for Numerical Methods in Engineering
%K 65n30-pdes-bvps-finite-elements 78m10-optics-electromagnetism-finite-element-method
%N 14
%P 2103-2130
%R 10.1002/nme.847
%T Hierarchic finite element bases on unstructured tetrahedral meshes
%U https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.847
%V 58
%X The problem of constructing hierarchic bases for finite element discretization of the spaces H 1, H (curl ), H (div ) and L 2 on tetrahedral elements is addressed. A simple and efficient approach to ensuring conformity of the approximations across element interfaces is described. Hierarchic bases of arbitrary polynomial order are presented. It is shown how these may be used to construct finite element approximations of arbitrary, non‐uniform, local order approximation on unstructured meshes of curvilinear tetrahedral elements.
@article{noauthororeditor,
abstract = {
The problem of constructing hierarchic bases for finite element discretization of the spaces H 1, H (curl ), H (div ) and L 2 on tetrahedral elements is addressed. A simple and efficient approach to ensuring conformity of the approximations across element interfaces is described. Hierarchic bases of arbitrary polynomial order are presented. It is shown how these may be used to construct finite element approximations of arbitrary, non‐uniform, local order approximation on unstructured meshes of curvilinear tetrahedral elements.},
added-at = {2020-06-03T02:03:53.000+0200},
author = {Ainsworth, Mark and Coyle, Joe},
biburl = {https://www.bibsonomy.org/bibtex/26d765c8abb91dbf720db8df4ff830cb0/gdmcbain},
doi = {10.1002/nme.847},
interhash = {167cb7c3622bf615fbad2d0b60c0a74b},
intrahash = {6d765c8abb91dbf720db8df4ff830cb0},
journal = {International Journal for Numerical Methods in Engineering},
keywords = {65n30-pdes-bvps-finite-elements 78m10-optics-electromagnetism-finite-element-method},
number = 14,
pages = {2103-2130},
timestamp = {2020-06-03T02:03:53.000+0200},
title = {Hierarchic finite element bases on unstructured tetrahedral meshes
},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.847},
volume = 58,
year = 2003
}