\newcommand{\boldx}{\mathbf{x}} \newcommand{\boldxi}{\boldsymbol{\xi}}

The quadrature formula is like the following:

## int1d#

### Notations#

$|D|$ is the measure of the edge $D$.

For a shake of simplicity, we denote: with $0\leq t\leq 1$; $\boldx=(1-t)\boldx_0+t\boldx_1$.

### qf1pE#

 1 int1d(Th, qfe=qf1pE)( ... ) 
or
 1 int1d(Th, qfe=qforder=2)( ... ) 

This quadrature formula is exact on $\P_1$.

\int_{D}{f(\boldx)} \approx |D|g\left(\frac{1}{2}\right)

### qf2pE#

 1 int1d(Th, qfe=qf2pE)( ... ) 
or
 1 int1d(Th, qfe=qforder=3)( ... ) 

This quadrature formula is exact on $\P_3$.

\int_{D}{f(\boldx)} \approx \frac{|D|}{2}\left( g\left( \frac{1+\sqrt{1/3}}{2} \right) + g\left( \frac{1-\sqrt{1/3}}{2} \right) \right)

### qf3pE#

 1 int1d(Th, qfe=qf3pE)( ... ) 
or
 1 int1d(Th, qfe=qforder=6)( ... ) 

This quadrature formula is exact on $\P_5$.

\int_{D}{f(\boldx)} \approx \frac{|D|}{18}\left( 5g\left( \frac{1+\sqrt{3/5}}{2} \right) + 8g\left( \frac{1}{2} \right) + 5g\left( \frac{1-\sqrt{3/5}}{2} \right) \right)

### qf4pE#

 1 int1d(Th, qfe=qf4pE)( ... ) 
or
 1 int1d(Th, qfe=qforder=8)( ... ) 

This quadrature formula is exact on $\P_7$.

\int_{D}{f(\boldx)} \approx \frac{|D|}{72}\left( (18-\sqrt{30})g\left( \frac{1-\frac{\sqrt{525+70\sqrt{30}}}{35}}{2} \right) + (18-\sqrt{30})g\left( \frac{1+\frac{\sqrt{525+70\sqrt{30}}}{35}}{2} \right) + (18+\sqrt{30})g\left( \frac{1-\frac{\sqrt{525-70\sqrt{30}}}{35}}{2} \right) + (18+\sqrt{30})g\left( \frac{1+\frac{\sqrt{525-70\sqrt{30}}}{35}}{2} \right) \right)

### qf5pE#

 1 int1d(Th, qfe=qf5pE)( ... ) 
or
 1 int1d(Th, qfe=qforder=10)( ... ) 

This quadrature formula is exact on $\P_9$.

\int_{D}{f(\boldx)} \approx |D|\left( \frac{(332-13\sqrt{70})}{1800}g\left( \frac{1-\frac{\sqrt{245+14\sqrt{70}}}{21}}{2} \right) + \frac{(332-13\sqrt{70})}{1800}g\left( \frac{1+\frac{\sqrt{245+14\sqrt{70}}}{21}}{2} \right) + \frac{64}{225}g\left( \frac{1}{2} \right) + \frac{(332+13\sqrt{70})}{1800}g\left( \frac{1-\frac{\sqrt{245-14\sqrt{70}}}{21}}{2} \right) + \frac{(332+13\sqrt{70})}{1800}g\left( \frac{1+\frac{\sqrt{245-14\sqrt{70}}}{21}}{2} \right) \right)

### qf1pElump#

 1 int1d(Th, qfe=qf1pElump)( ... ) 

This quadrature formula is exact on $\P_2$.

\int_{D}{f(\boldx)} \approx \frac{|D|}{2}\left( g\left( 0 \right) + g\left( 1 \right) \right)

## int2d#

### qf1pT#

$\codered$

### qf2pT#

$\codered$

### qf5pT#

$\codered$

### qf1pTlump#

$\codered$

### qf2pT4P1#

$\codered$

### qf7pT#

$\codered$

### qf9pT#

$\codered$

## int3d#

### qfV1#

$\codered$

### qfV2#

$\codered$

### qfV5#

$\codered$

### qfV1lump#

$\codered$