def runTest(self):
# solve Poisson by standard P1 method
# and P1(dg) interior penalty method.
#
# this will test interior facet assembly and normal
# vectors.
from spfem.mesh import MeshTri
from spfem.asm import AssemblerElement
from spfem.element import ElementTriP1, ElementTriDG
from spfem.utils import direct
import numpy as np
m = MeshTri()
m.refine(3)
e = ElementTriDG(ElementTriP1())
e1 = ElementTriP1()
a = AssemblerElement(m, e)
a1 = AssemblerElement(m, e1)
b1 = AssemblerElement(m, e1, e)
A = a.iasm(lambda du, dv: du[0]*dv[0] + du[1]*dv[1])
M = a.iasm(lambda u, v: u*v)
b = a.iasm(lambda v, x: np.sin(2.0*np.pi*x[0])*v)
B1 = a.fasm(lambda u1,u2,v1,v2,h: 1/h*(u1-u2)*(v1-v2), interior=True)
B2 = a.fasm(lambda u,v,h: 1/h*u*v)
B=B1+B2
C1 = a.fasm(lambda du1,du2,v1,v2,n: 0.5*(du1[0]*n[0]*v1 - du2[0]*n[0]*v2
+ du1[1]*n[1]*v1 - du2[1]*n[1]*v2), interior=True)
C2 = a.fasm(lambda du,v,n: (du[0]*n[0]+du[1]*n[1])*v)
C=C1+C2
D = C+C.T
eps = 1e-3
eta = 1e5
x = direct(A + eta*B - 0*D, b)
K = a1.iasm(lambda du, dv: du[0]*dv[0] + du[1]*dv[1])
f = a1.iasm(lambda v, x: np.sin(2.0*np.pi*x[0])*v)
y = direct(K, f, I=m.interior_nodes())
P = b1.iasm(lambda u,v: u*v)
self.assertAlmostEqual(np.linalg.norm(x-direct(M,P*y)),0,places=4)
