class ConvergenceLineP1(ConvergenceQ1):
def create_basis(self, m):
e = ElementLineP1()
return InteriorBasis(m, e)
def setUp(self):
self.mesh = MeshLine()
self.mesh.refine(3)
class ConvergenceLineP2(ConvergenceQ1):
rateL2 = 3.0
rateH1 = 2.0
def create_basis(self, m):
e = ElementLineP2()
return InteriorBasis(m, e)
def setUp(self):
self.mesh = MeshLine()
self.mesh.refine(3)
def runTest(self):
m = MeshLine(np.linspace(0., 1.))
m.refine(2)
ib = InteriorBasis(m, self.e)
fb = FacetBasis(m, self.e)
@LinearForm
def boundary_flux(v, w):
return v * (w.x[0] == 1) - v * (w.x[0] == 0)
L = asm(laplace, ib)
M = asm(mass, ib)
b = asm(boundary_flux, fb)
u = solve(L + 1e-6 * M, b)
np.testing.assert_array_almost_equal(u[ib.nodal_dofs[0]], m.p[0] - .5, -4)
def runTest(self):
m = MeshLine(np.linspace(0., 1.))
m.refine(2)
ib = InteriorBasis(m, self.e)
fb = FacetBasis(m, self.e)
@LinearForm
def boundary_flux(v, w):
return v * (w.x[0] == 1.)
L = asm(laplace, ib)
b = asm(boundary_flux, fb)
D = m.nodes_satisfying(lambda x: x == 0.0)
I = ib.complement_dofs(D) # noqa E741
u = solve(*condense(L, b, I=I)) # noqa E741
np.testing.assert_array_almost_equal(u[ib.nodal_dofs[0]], m.p[0], -10)
def runTest(self):
m = MeshLine(np.linspace(0., 1.))
m.refine(2)
e = ElementLineP1()
ib = InteriorBasis(m, e)
fb = FacetBasis(m, e)
@linear_form
def boundary_flux(v, dv, w):
return v * (w.x[0] == 1) - v * (w.x[0] == 0)
L = asm(laplace, ib)
M = asm(mass, ib)
b = asm(boundary_flux, fb)
u = solve(L + 1e-6 * M, b)
self.assertTrue(np.sum(np.abs(u - m.p[0, :] + 0.5)) < 1e-4)
def runTest(self):
m = MeshLine(np.linspace(0., 1.))
m.refine(2)
e = ElementLineP1()
ib = InteriorBasis(m, e)
fb = FacetBasis(m, e)
@linear_form
def boundary_flux(v, dv, w):
return -v * (w.x[0] == 1.)
L = asm(laplace, ib)
b = asm(boundary_flux, fb)
D = m.nodes_satisfying(lambda x: x == 0.0)
I = ib.complement_dofs(D) # noqa E741
u = solve(*condense(L, b, I=I)) # noqa E741
self.assertTrue(np.sum(np.abs(u + m.p[0, :])) < 1e-10)
def runTest(self):
m = MeshLine(np.linspace(0., 1.))
m.refine(2)
ib = InteriorBasis(m, self.e)
m.define_boundary('left' ,lambda x: x[0] == 0.0)
m.define_boundary('right', lambda x: x[0] == 1.0)
fb = FacetBasis(m, self.e, facets=m.boundaries['right'])
@LinearForm
def boundary_flux(v, w):
return -w.x[0] * v
L = asm(laplace, ib)
b = asm(boundary_flux, fb)
D = ib.find_dofs()['left'].all()
I = ib.complement_dofs(D) # noqa E741
u = solve(*condense(L, b, I=I)) # noqa E741
np.testing.assert_array_almost_equal(u[ib.nodal_dofs[0]], -m.p[0], -10)
