A family of 3D continuously differentiable finite elements on tetrahedral grids

A family of continuously differentiable piecewise polynomials of degree 9 and higher, on general tetrahedral grids, is constructed, by simplifying and extending the P 9 element of Ženišek. A mathematical justification and numerical tests are presented. The current computing power is still limited fo...

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Bibliographic Details
Published in:Applied numerical mathematics 2009, Vol.59 (1), p.219-233
Main Author: Zhang, Shangyou
Format: Article
Language:English
Subjects:
3D biharmonic equation
Continuously differentiable finite element
Divergence-free element
Exact sciences and technology
Global analysis, analysis on manifolds
High order element
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Stokes equations
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:A family of continuously differentiable piecewise polynomials of degree 9 and higher, on general tetrahedral grids, is constructed, by simplifying and extending the P 9 element of Ženišek. A mathematical justification and numerical tests are presented. The current computing power is still limited for the computation with 3D C 1 finite elements in general. The construction here mainly serves the purposes of understanding and ensuring the approximation properties of C 1 finite elements spaces on tetrahedral grids. In particular, this construction indicates that the 3D divergence-free C 0 - P k elements have the full order of approximation for any degree k ⩾ 8 .
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2008.02.002