High-order finite elements on pyramids. II: unisolvency and exactness

Details High-order finite elements on pyramids. II: unisolvency and exactness High-order finite elements on pyramids. II: unisolvency and exactness

2010-06-27

arxiv.org/abs/1006.5240v2

Mathematics

Numerical Analysis

The two parts of this paper have been re-combined into one manuscript so part II has been withdrawn. The full version is now a

Scientific paper

We present degrees of freedom to accompany the approximation spaces already presented in a companion paper and thus complete the definition of families of high-order conforming finite elements on pyramids for the spaces of the de Rham complex. We prove that the elements are unisolvent; are compatible with conventional tetrahedral and hexahedral elements; satisfy a commuting diagram property and contain high-degree polynomials. We also tabulate shape functions for each element.

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