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Hierarchic finite element bases on unstructured tetrahedral meshes

Ainsworth, M. and Coyle, J. (2003) Hierarchic finite element bases on unstructured tetrahedral meshes. International Journal for Numerical Methods in Engineering, 58 (14). pp. 2103-2130. ISSN 0029-5981

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Abstract

The problem of constructing hierarchic bases for finite element discretization of the spaces H1, H(curl), H(div) and L2 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.