Why the solution of ft01 example break down on finer meshes?

1

Hi everyone,

I am new to FEniCS and currently I am trying to learn the basics on available examples.
When I was playing with the ft01 example (Poisson equation with Dirichlet conditions) I realized that when the number of mesh cells is increased even slightly from the default number, the solution is breaking down.

For n = 10 (number of cells in a horizontal and vertical direction) I received correct output:
n_10
but for higher numers, for example n = 15 the output is rather different and obviously not correct:
n_15

I have no idea why this strange behaviour occurs. Therefore the question is: Did I make an error when modifying the original code to run it in the Jupyter Lab or is something wrong with my installation of FEniCS?

The code I am running looks like this:

    from __future__ import print_function
    from fenics import *
    import numpy as np
    import matplotlib.pyplot as plt

    def boundary(x, on_boundary):
        return on_boundary

    # Create mesh and define function space
    n = 15
    mesh = UnitSquareMesh(n, n)
    V = FunctionSpace(mesh, 'CG', 1)

    # Define boundary condition
    u_D = Expression('1 + x[0]*x[0] + 2*x[1]*x[1]', degree=2)

    bc = DirichletBC(V, u_D, boundary)

    # Define variational problem
    u = TrialFunction(V)
    v = TestFunction(V)
    f = Constant(-6.0)
    a = dot(grad(u), grad(v))*dx
    L = f*v*dx

    # Compute solution
    u = Function(V)
    solve(a == L, u, bc)

    # Plot solution and mesh
    plt.colorbar(plot(u))
    plt.rcParams["figure.figsize"] = (5, 5)

The version of FEniCS: 2018.1.0
Installation: through Anaconda on Ubuntu on Windows. I run the code in Jupyter Lab.

2

Running your attached example (Removing the figsize command, and plotting the mesh on top of the solution field in docker do not reproduce the error docker run -ti -v $(pwd):/home/fenics/shared -w /home/fenics/shared/ --rm quay.io/fenicsproject/stable:2018.1.0
u

3

Thanks for your answer,
I initially tried to avoid Docker because I’m more familiar with Ubuntu on Windows. But I instaled Docker, run the code on the container and it works just fine there. So I guess that something is definitely wrong with my installation of FEniCS on Ubuntu on Windows. However, Docker is actually a lot simpler to use than I initially thought, so I will just stay there :slight_smile: