Thank you for your any help !!! I appreciate it.
I know how to solve poisson problem using AdaptiveLinearVariationalSolver().
But how do I get the error and convervence rate at every refinement step ?
My code is below:
from dolfin import *
# Create mesh and define function space
mesh = UnitSquareMesh(8, 8)
V = FunctionSpace(mesh, "Lagrange", 1)
# Define boundary condition
u0 = Function(V)
bc = DirichletBC(V, u0, "x[0] < DOLFIN_EPS || x[0] > 1.0 - DOLFIN_EPS")
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
f = Expression("10*exp(-(pow(x[0] - 0.5, 2) + pow(x[1] - 0.5, 2)) / 0.02)",
degree=1)
g = Expression("sin(5*x[0])", degree=1)
a = inner(grad(u), grad(v))*dx()
L = f*v*dx() + g*v*ds()
# Define function for the solution
u = Function(V)
# Define goal functional (quantity of interest)
M = u*dx()
# Define error tolerance
tol = 1.e-4
# Solve equation a = L with respect to u and the given boundary
# conditions, such that the estimated error (measured in M) is less
# than tol
problem = LinearVariationalProblem(a, L, u, bc)
solver = AdaptiveLinearVariationalSolver(problem, M)
solver.parameters["error_control"]["dual_variational_solver"]["linear_solver"] = "cg"
solver.solve(tol)
solver.summary()
# Plot solution(s)
plot(u.root_node(), title="Solution on initial mesh")
plot(u.leaf_node(), title="Solution on final mesh")
plot(mesh.root_node())
plot(mesh.leaf_node())
interactive()
