2D FEM using Firedrake¶
Copyright (C) 2026 Andreas Kloeckner
MIT License
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In [1]:
from firedrake import *
import numpy as np
import numpy.linalg as la
import firedrake.mesh as fd_mesh
import matplotlib.pyplot as plt
In [2]:
mesh = Mesh("blob.msh")
triplot(mesh)
Out[2]:
[<matplotlib.collections.PolyCollection at 0x7fca327525a0>]
In [3]:
V = FunctionSpace(mesh, 'Lagrange', 1)
In [18]:
x = SpatialCoordinate(mesh)
f = conditional(le(x[0], 0), 4, -8)
In [19]:
g = interpolate(-2*x[0], V)
bc = DirichletBC(V, g, "on_boundary")
# bc = DirichletBC(V, 0.0, "on_boundary")
In [20]:
u = TrialFunction(V)
v = TestFunction(V)
v
Out[20]:
Argument(WithGeometry(FunctionSpace(<firedrake.mesh.MeshTopology object at 0x7fca34523380>, FiniteElement('Lagrange', triangle, 1), name=None), Mesh(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), 1)), 0, None)
In [21]:
a = inner(grad(u), grad(v))*dx
L = f*v*dx
In [22]:
U = Function(V)
solve(a == L, U, bc)
In [23]:
tricontourf(U)
Out[23]:
<matplotlib.tri._tricontour.TriContourSet at 0x7fca237d0110>
In [24]:
fig = plt.figure(figsize=(10, 10))
axes = fig.add_subplot(111, projection='3d')
trisurf(U, axes=axes)
Out[24]:
<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x7fca238ee930>
In [ ]: