an encyclopedia of finite element definitions

# Dual polynomial

 Abbreviated names dual Orders $$0\leqslant k\leqslant 1$$ Reference elements dual polygon Number of DOFs dual polygon(n): $$\begin{cases}1&k=0\\n&k=1\end{cases}$$ Mapping identity continuity Discontinuous. ($$n=0$$)Function values are continuous. ($$n=1$$) Notes These elements are defined on the barycentric dual grid. These elements are defined as a linear combination of Lagrange basis functions on the fine grid. Categories Scalar-valued elements

## Implementations

 Bempp "DUAL"↓ Show Bempp examples ↓ Symfem "dual"↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations.

## Examples

 dual polygon(6)order 0 (click to view basis functions) dual polygon(4)order 1 (click to view basis functions) dual polygon(5)order 1 (click to view basis functions) dual polygon(6)order 1 (click to view basis functions)
• Buffa, Annalisa and Christiansen, Snorre H. A dual finite element complex on the barycentric refinement, Mathematics of Computation 76, 1743–1769, 2007. [DOI: 10.1016/j.crma.2004.12.022] [BibTeX]

## DefElement stats

 Element added 24 January 2021 Element last updated 16 September 2023