def setup_error_monitor(true, history, path=''):
'''We measure error in H1 and L2 for simplicity'''
from common import monitor_error, H1_norm, L2_norm
# Note we produce u1, u2, and p error. It is more natural to have
# broken H1 norm so reduce the first 2 errors to single number
reduction = lambda e: None if e is None else [sqrt(e[0]**2 + e[1]**2), e[-1]]
return monitor_error(true, [H1_norm, H1_norm, L2_norm], history, reduction, path=path)
def setup_error_monitor(true, history, path=''):
'''We measure error in H1 and L2 for simplicity'''
from common import monitor_error, H1_norm, L2_norm
# Note we produce u1, u2, and p error. It is more natural to have
# broken H1 norm so reduce the first 2 errors to single number
reduction = lambda e: None if e is None else [sqrt(e[0]**2 + e[1]**2), e[-1]]
return monitor_error(true, [H1_norm, H1_norm, L2_norm], history, reduction, path=path)
def setup_error_monitor(true, history, path=''):
'''We measure error V1 x Q1, V2 x Q2, L2(instead of fractional)'''
from common import monitor_error, H1_norm, L2_norm, Hdiv_norm
# First stokes, then darcy pressure
reduction = lambda e: None if e is None else [sqrt(e[0]**2 + e[2]**2), e[1]]
return monitor_error(true,
# u1, p, p1
[H1_norm, H1_norm, L2_norm],
history, path=path, reduction=reduction)
def setup_error_monitor(true, history, path=''):
'''We measure error V1 x Q1, V2 x Q2, L2(instead of fractional)'''
from common import monitor_error, H1_norm, L2_norm, Hdiv_norm
# Note we produce u1, u2, and p error. It is more natural to have
# broken H1 norm so reduce the first 2 errors to single number
reduction = lambda e: None if e is None else [sqrt(e[0]**2 + e[1]**2), e[-1]]
return monitor_error(true,
[H1_norm, L2_norm, Hdiv_norm, L2_norm, L2_norm],
history, path=path)
def setup_error_monitor(true, history, path=''):
'''We measure error V1 x Q1, V2 x Q2, L2(instead of fractional)'''
from common import monitor_error, H1_norm, L2_norm, Hdiv_norm
# Note we produce u1, u2, and p error. It is more natural to have
# broken H1 norm so reduce the first 2 errors to single number
reduction = lambda e: None if e is None else [
sqrt(e[0]**2 + e[1]**2), e[-1]
]
return monitor_error(true, [H1_norm, L2_norm, Hdiv_norm, L2_norm, L2_norm],
history,
path=path)
def setup_error_monitor(true, history, path=''):
'''We measure error V1 x Q1, V2 x Q2, L2(instead of fractional)'''
from common import monitor_error, H1_norm, L2_norm, Hdiv_norm
# First stokes, then darcy pressure
reduction = lambda e: None if e is None else [
sqrt(e[0]**2 + e[1]**2), e[2]
]
return monitor_error(
true,
# u1, p, p1
[H1_norm, L2_norm, H1_norm],
history,
path=path,
reduction=reduction)
def setup_error_monitor(true, history, path=''):
'''We measure error in Hdiv and L2 for simplicity'''
from common import monitor_error, Hdiv_norm, L2_norm
from math import sqrt
# Note we produce sigma1, sigma2 u1, u2, and p error. But this is just
# so that it is easier to compute error as the true solution is
# discontinuous. So we compute on subdomain and then reduce
reduction = lambda e: None if e is None else [sqrt(e[0]**2 + e[1]**2), # Hdiv
sqrt(e[2]**2 + e[3]**2), # L2
e[-1]]
return monitor_error(true,
[Hdiv_norm, Hdiv_norm, L2_norm, L2_norm, L2_norm],
history,
reduction,
path=path)
def setup_error_monitor(true, history, path=''):
'''We measure error in L2 and L2, L2 for simplicity'''
# L2 on velocity because eps -> 0 H1 does not make sense
from common import monitor_error, H1_norm, L2_norm
# Now for the multiplier, since we really know the exact solution
# only on pieces of the mesh, we will do things manually
#
def foo(u, uh):
mesh = uh.function_space().mesh()
cell_f = MeshFunction('size_t', mesh, mesh.topology().dim(), 0)
# Mark pieces
# CompiledSubDomain('near(x[1], 1)').mark(cell_f, 0)
CompiledSubDomain('near(x[0], 0)').mark(cell_f, 1)
CompiledSubDomain('near(x[1], 0)').mark(cell_f, 2)
CompiledSubDomain('near(x[0], 1)').mark(cell_f, 3)
dX = Measure('dx', domain=mesh, subdomain_data=cell_f)
error = sum(inner(uj-uh, uj-uh)*dX(j) for j, uj in enumerate(u))
return sqrt(assemble(error))
return monitor_error(true, [L2_norm, L2_norm, foo], history, path=path)
def setup_error_monitor(true, history, path=''):
'''We measure error in L2 and L2, L2 for simplicity'''
# L2 on velocity because eps -> 0 H1 does not make sense
from common import monitor_error, H1_norm, L2_norm
# Now for the multiplier, since we really know the exact solution
# only on pieces of the mesh, we will do things manually
#
def foo(u, uh):
mesh = uh.function_space().mesh()
cell_f = MeshFunction('size_t', mesh, mesh.topology().dim(), 0)
# Mark pieces
# CompiledSubDomain('near(x[1], 1)').mark(cell_f, 0)
CompiledSubDomain('near(x[0], 0)').mark(cell_f, 1)
CompiledSubDomain('near(x[1], 0)').mark(cell_f, 2)
CompiledSubDomain('near(x[0], 1)').mark(cell_f, 3)
dX = Measure('dx', domain=mesh, subdomain_data=cell_f)
error = sum(inner(uj - uh, uj - uh) * dX(j) for j, uj in enumerate(u))
return sqrt(assemble(error))
return monitor_error(true, [L2_norm, L2_norm, foo], history, path=path)
def setup_error_monitor(true, history, path=''):
'''We measure error in H1 and L2, L2 for simplicity'''
from common import monitor_error, H1_norm, L2_norm
return monitor_error(true, [H1_norm, L2_norm, L2_norm], history, path=path)
def setup_error_monitor(true, history, path=''):
'''We measure error in H1 and L2 for simplicity'''
from common import monitor_error, H1_norm, L2_norm
return monitor_error(true, [H1_norm, L2_norm], history, path=path)
def setup_error_monitor(true, history, path=''):
'''TODO'''
from common import monitor_error, H1_norm, L2_norm
return monitor_error(true, [], history, path=path)
def setup_error_monitor(true, history, path=''):
'''We measure error in H1 and abs norm for the multiplier'''
from common import monitor_error, H1_norm, linf_norm
return monitor_error(true, [H1_norm, linf_norm], history, path=path)
def setup_error_monitor(true, history, path=''):
'''TODO'''
from common import monitor_error, H1_norm, L2_norm
return monitor_error(true, [], history, path=path)
def setup_error_monitor(true, history, path=''):
'''We measure error in H1 and abs norm for the multiplier'''
from common import monitor_error, H1_norm, linf_norm
return monitor_error(true, [H1_norm, linf_norm], history, path=path)
