an encyclopedia of finite element definitions
Degree 1 serendipity on a quadrilateral
◀ Back to serendipity definition page
- \(R\) is the reference quadrilateral. The following numbering of the subentities of the reference is used:
- \(\mathcal{V}\) is spanned by: \(1\), \(x\), \(y\), \(x y\)
- \(\mathcal{L}=\{l_0,...,l_{3}\}\)
- Functionals and basis functions:
\(\displaystyle l_{0}:v\mapsto v(0,0)\)
\(\displaystyle \phi_{0} = x y - x - y + 1\)
This DOF is associated with vertex 0 of the reference element.
\(\displaystyle \phi_{0} = x y - x - y + 1\)
This DOF is associated with vertex 0 of the reference element.
\(\displaystyle l_{1}:v\mapsto v(1,0)\)
\(\displaystyle \phi_{1} = x \left(1 - y\right)\)
This DOF is associated with vertex 1 of the reference element.
\(\displaystyle \phi_{1} = x \left(1 - y\right)\)
This DOF is associated with vertex 1 of the reference element.
\(\displaystyle l_{2}:v\mapsto v(0,1)\)
\(\displaystyle \phi_{2} = y \left(1 - x\right)\)
This DOF is associated with vertex 2 of the reference element.
\(\displaystyle \phi_{2} = y \left(1 - x\right)\)
This DOF is associated with vertex 2 of the reference element.
\(\displaystyle l_{3}:v\mapsto v(1,1)\)
\(\displaystyle \phi_{3} = x y\)
This DOF is associated with vertex 3 of the reference element.
\(\displaystyle \phi_{3} = x y\)
This DOF is associated with vertex 3 of the reference element.