def testLaplacian(self):
''' Use finite differences to check the Lapalcian calculations'''
N = 6
h = 1E-4
x,w = puq.trianglequadrature(5)
for k in range(1,N):
v = pup.DubinerTriangle(k, x).values()
L = pup.laplacian(k)
Lv = np.dot(v, L)
Lhv = (sum([pup.DubinerTriangle(k, x+xh).values() for xh in ([0,h],[0,-h],[h,0],[-h,0])]) - 4*v)/(h**2)
np.testing.assert_almost_equal(Lv, Lhv, decimal=3)
def testLaplaceZero(self):
''' Test that the linear polynomials will have a zero laplacian'''
L = pup.laplacian(1)
np.testing.assert_almost_equal(L, 0, decimal=5)