Why do I get this error when computing an auto-adaptive method for the mixed Poisson equation?
11 weeks ago by
I am currently working on mixed formulations for the linear elasticity equations and I wish to implement an adaptive scheme. I tried the adaptive solver implemented in FEniCS and got some errors which I do not understand. I obtain the same errors when solving the mixed Poisson equation. I have constructed a short working example based on the mixed formulation for the Poisson equation given in this example.
The error message that pops up is the following one: "Replacement expressions must have the same shape as what they replace". What is the source of this error?
from dolfin import * # Create mesh mesh = UnitSquareMesh(32, 32) # Define function spaces and mixed (product) space BDM = FiniteElement("BDM", mesh.ufl_cell(), 1) DG = FiniteElement("DG", mesh.ufl_cell(), 0) W = FunctionSpace(mesh, BDM * DG) # Define trial and test functions (sigma, u) = TrialFunctions(W) (tau, v) = TestFunctions(W) w = Function(W) # Define source function f = Expression("10*exp(-(pow(x - 0.5, 2) + pow(x - 0.5, 2)) / 0.02)", degree = 4) # Define variational form a = (dot(sigma, tau) + div(tau)*u + div(sigma)*v)*dx L = - f*v*dx # Define function G such that G \cdot n = g class BoundarySource(Expression): def __init__(self, mesh, degree): self.mesh = mesh self.degree = degree def eval_cell(self, values, x, ufc_cell): cell = Cell(self.mesh, ufc_cell.index) n = cell.normal(ufc_cell.local_facet) g = sin(5*x) values = g*n values = g*n def value_shape(self): return (2,) G = BoundarySource(mesh, degree = 4) # Define essential boundary def boundary(x): return x < DOLFIN_EPS or x > 1.0 - DOLFIN_EPS bc = DirichletBC(W.sub(0), G, boundary) # Define goal functional (quantity of interest) M = w*dx # Define error tolerance tol = 1.e-3 # Solve equation a = L with respect to w and the given boundary # conditions, such that the estimated error (measured in M) is less # than tol problem = LinearVariationalProblem(a, L, w, bc) solver = AdaptiveLinearVariationalSolver(problem, M) solver.parameters["error_control"]["dual_variational_solver"]["linear_solver"] = "cg" solver.parameters["error_control"]["dual_variational_solver"]["symmetric"] = True solver.solve(tol) solver.summary()
** Dolfin version: 2016.2.0
Community: FEniCS Project
Please login to add an answer/comment or follow this question.