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## [Getfem-users] number of Newton-Cotes points

 From: Edouard Oudet Subject: [Getfem-users] number of Newton-Cotes points Date: Wed, 16 Jan 2019 20:19:49 +0100 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:60.0) Gecko/20100101 Thunderbird/60.2.1

```Dear all,

```
I studied a simple situation : a triangular mesh and defined a MeshIm class based on Newton-Cotes methods of degree "degi". I expected for every triangle to have (degi + 1) * (degi + 2) / 2 quadrature points.
```
```
Surprisingly for me, the following illustration below shows that for a degree 4 for instance, I obtain 12 quadrature points which is different from 15.. It seems that some vertices of the triangle are not taken into account.
```
```
Is it because the weights of these points is 0.? Or perhaps I didn't call the class in the right way?
```
Any comments are welcome,

best,

Edouard.

/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

import getfem
import numpy as np

def nb_imdata(degi):
# creation mesh / fem / im
NX = 6
```
tmesh = getfem.Mesh('regular_simplices', np.arange(0, 1 + 1. / NX, 1. / NX),                                              np.arange(0, 1 + 1. / NX, 1. / NX))
```    tmeshfem = getfem.MeshFem(tmesh, 1)
tmeshfem.set_fem(getfem.Fem('FEM_PK(2, 2)'))
```
tmeshim = getfem.MeshIm(tmesh, getfem.Integ('IM_NC(2,' + str(degi) + ')'))
```    #print tmeshim.im_nodes()
print 'degree ', degi, '|', \
'nb of quad points ', tmeshim.im_nodes(2).shape, '|', \
'expected          ', ((degi + 1) * (degi + 2) / 2)

for  k in range(3, 10):
nb_imdata(k)

```

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