Degree 2 enriched Galerkin on a quadrilateral

• \(R\) is the reference quadrilateral. The following numbering of the subentities of the reference is used:

• Basis functions:

\(\displaystyle \phi_{0} = 4 x^{2} y^{2} - 6 x^{2} y + 2 x^{2} - 6 x y^{2} + 9 x y - 3 x + 2 y^{2} - 3 y + 1\)

\(\displaystyle \phi_{1} = x \left(4 x y^{2} - 6 x y + 2 x - 2 y^{2} + 3 y - 1\right)\)

\(\displaystyle \phi_{2} = y \left(4 x^{2} y - 2 x^{2} - 6 x y + 3 x + 2 y - 1\right)\)

\(\displaystyle \phi_{3} = x y \left(4 x y - 2 x - 2 y + 1\right)\)

\(\displaystyle \phi_{4} = 4 x \left(- 2 x y^{2} + 3 x y - x + 2 y^{2} - 3 y + 1\right)\)

\(\displaystyle \phi_{5} = 4 y \left(- 2 x^{2} y + 2 x^{2} + 3 x y - 3 x - y + 1\right)\)

\(\displaystyle \phi_{6} = 4 x y \left(- 2 x y + 2 x + y - 1\right)\)

\(\displaystyle \phi_{7} = 4 x y \left(- 2 x y + x + 2 y - 1\right)\)

\(\displaystyle \phi_{8} = 16 x y \left(x y - x - y + 1\right)\)

\(\displaystyle \phi_{9} = 1\)