Shape Function in H1 element

General
1

I have generated one tetrahedron element.

from netgen.csg import Pnt
from netgen.meshing import Element3D, Element2D, MeshPoint, FaceDescriptor, Mesh
mesh = Mesh()
mesh.dim = 3
dom = {}
dom[1] = mesh.Add(FaceDescriptor(bc=1,domin=1,surfnr=1))
v = []
v.append(mesh.Add(MeshPoint(Pnt(0,0,0))))
v.append(mesh.Add(MeshPoint(Pnt(1,0,0))))
v.append(mesh.Add(MeshPoint(Pnt(0,1,0))))
v.append(mesh.Add(MeshPoint(Pnt(0,0,1))))
mesh.Add(Element2D(dom[1], [v[0],v[1],v[2]]))
mesh.Add(Element2D(dom[1], [v[0],v[1],v[3]]))
mesh.Add(Element2D(dom[1], [v[1],v[2],v[3]]))
mesh.Add(Element2D(dom[1], [v[2],v[0],v[3]]))
mesh.Add(Element3D(dom[1], v))
import ngsolve
mesh = ngsolve.Mesh(mesh)

When I draw the function like

from ngsolve import *
fes1 = H1(mesh, order=3)
gfA = GridFunction(fes1)
ndof=fes1.ndof;
print([ndof])
from ngsolve.webgui import Draw
for m in [4,5]:
    print("Shape function ", m)
    gfA.vec[:] = 0
    gfA.vec[m] = 1
    Draw (gfA)

We can see contour plots when m=4, but not m=5. Are there any reason for this?

2

In my opinion it is a Drawing issue. Using a finer mesh to draw the Shape functions of the coarse mesh results in good plots for me:

  from netgen.csg import *
  from netgen.meshing import Element3D, Element2D, MeshPoint, FaceDescriptor, Mesh
  
  meshCoarse = Mesh()
  from ngsolve import *
  mesh.dim = 3
  dom = {}
  dom[1] = meshCoarse.Add(FaceDescriptor(bc=1,domin=1,surfnr=1))
  v = []
  v.append(meshCoarse.Add(MeshPoint(Pnt(0,0,0))))
  v.append(meshCoarse.Add(MeshPoint(Pnt(1,0,0))))
  v.append(meshCoarse.Add(MeshPoint(Pnt(0,1,0))))
  v.append(meshCoarse.Add(MeshPoint(Pnt(0,0,1))))
  meshCoarse.Add(Element2D(dom[1], [v[0],v[1],v[2]]))
  meshCoarse.Add(Element2D(dom[1], [v[0],v[1],v[3]]))
  meshCoarse.Add(Element2D(dom[1], [v[1],v[2],v[3]]))
  meshCoarse.Add(Element2D(dom[1], [v[2],v[0],v[3]]))
  meshCoarse.Add(Element3D(dom[1], v))
  
  meshCoarse = Mesh(meshCoarse)
  
  bottom = Plane(Pnt(0, 0, 0), Vec(0, 0, -1))
  left = Plane(Pnt(0, 0, 0), Vec(-1, 0, 0))
  front = Plane(Pnt(0, 0, 0), Vec(0, -1, 0))
  diag = Plane(Pnt(0, 0, 1), Vec(1, 1, 1))
  tet = bottom*left*front*diag
  
  geo = CSGeometry()
  geo.Add (tet)
  
  meshFine = Mesh(geo.GenerateMesh(maxh=0.2))
  
  
  print("Vol mesh1", Integrate(1, meshCoarse))
  print("Vol meshFine", Integrate(1, meshFine))
  
  
  
  
  fes1 = H1(meshCoarse, order=3)
  gfA = GridFunction(fes1)
  ndof=fes1.ndof;
  print([ndof])
  from ngsolve.webgui import Draw

  
  print(len(gfA.vec))
  
  
  
  for m in [0, 1, 2, 3, 4,5]:
      print("Shape function ", m)
      gfA.vec[:] = 0
      gfA.vec[m] = 1
      print("int mesh1", Integrate(gfA, meshCoarse))
      print("int meshFine", Integrate(gfA, meshFine))
      
      Draw(gfA, meshFine, "test")

image

3

yes this is just lacking visualization options. For these edge functions you can also give the order=3 parameter

Draw(gfA, order=3)

image
image785×511 6.25 KB

but higher order are not yet possible in webgui. Also subdivision is still missing (but hopefully coming soon). For this you could use the old desktop gui for now