[Getfem-users] number of Newton-Cotes points

[Edouard Oudet]

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.

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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)[0].shape[0], '|', \
          'expected          ', ((degi + 1) * (degi + 2) / 2)


for  k in range(3, 10):
    nb_imdata(k)