Polynomial Liftings on a Tetrahedron and Applications to the h-p Version of the Finite Element Method in Three Dimensions

We construct a stable polynomial lifting on a tetrahedron, given polynomial traces defined on its faces satisfying continuity conditions along the edges. We apply this result to establish the optimal convergence rate of the h-p version of the finite element method in dimension three assuming the sol...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1997-02, Vol.34 (1), p.282-314
Main Author: Munoz-Sola, Rafael
Format: Article
Language:English
Subjects:
Approximation
Exact sciences and technology
Finite element analysis
Finite element method
Functional analysis
Interpolation
Mathematical analysis
Mathematics
Methods
Norms
Numerical analysis
Numerical analysis. Scientific computation
Parameterization
Partial differential equations, boundary value problems
Polynomials
Rhytidoplasty
Sciences and techniques of general use
Sobolev spaces
Tetrahedrons
Vertices
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Description
Summary:We construct a stable polynomial lifting on a tetrahedron, given polynomial traces defined on its faces satisfying continuity conditions along the edges. We apply this result to establish the optimal convergence rate of the h-p version of the finite element method in dimension three assuming the solution to be regular.
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142994267552