The accompanying Jupyter notebook can be obtained here 1_built_in_mesh

Built in meshes

FEniCS provides built-in capabilities to generate various types of meshes, allowing users to focus on the core of their simulations. Please visit the official documentation link provided to learn how to modify the mesh. After familiarizing yourself with the process, return here to implement the changes and visualize the updated results.

Click here to find out more about meshes

from dolfin import *

Change this portion of the code to: 1. Make a 2D unit square mesh. 2. Make a rectangle mesh with dimension \(2 \times 1\)

mesh = IntervalMesh(30, 0, 1)

U = FunctionSpace(mesh, "CG", 1)

u_D = Constant(0.0)
boundary = CompiledSubDomain("on_boundary")
bc = DirichletBC(U, u_D, boundary)
u, v = TrialFunction(U), TestFunction(U)

a = inner(grad(u), grad(v)) * dx
f_expr = Expression("pi*pi*sin(pi*x[0])", pi=np.pi, degree=2)
L = f_expr * v * dx

u_sol = Function(U, name = "field")
solve(a == L, u_sol, bc)

with XDMFFile("output/result.xdmf") as outfile:
    outfile.write(u_sol)