File: poisson.py

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from basix.ufl import element
from ufl import (
    Coefficient,
    Constant,
    FunctionSpace,
    Mesh,
    TestFunction,
    TrialFunction,
    dx,
    grad,
    inner,
)

e = element("Lagrange", "tetrahedron", 2)
coord_element = element("Lagrange", "tetrahedron", 1, shape=(3,))
mesh = Mesh(coord_element)

V = FunctionSpace(mesh, e)

u = TrialFunction(V)
v = TestFunction(V)
f = Coefficient(V)
kappa = Constant(mesh)

a = kappa * inner(grad(u), grad(v)) * dx