# Code in this cell makes plots appear an appropriate size and resolution in the browser window
%matplotlib widget
%config InlineBackend.figure_format = 'svg'

import matplotlib.pyplot as plt

plt.rcParams['figure.figsize'] = (11, 6)

from firedrake import *
mesh = UnitSquareMesh(10, 10)
V = FunctionSpace(mesh, "Lagrange", 1)

x, y = SpatialCoordinate(mesh)
u_exact = sin(pi*x)*sin(pi*y)
f = 2*pi**2*u_exact

u = TrialFunction(V)
v = TestFunction(V)
a = dot(grad(u), grad(v))*dx
L = f*v*dx

?DirichletBC

boundary_ids = (1, 2, 3, 4)
bcs = DirichletBC(V, 0, boundary_ids)

uh = Function(V)
solve(a == L, uh, bcs=bcs, solver_parameters={"ksp_type": "cg", "pc_type": "none"})

# NBVAL_IGNORE_OUTPUT
from firedrake.pyplot import tripcolor

fig, axes = plt.subplots()
collection = tripcolor(uh, axes=axes)
fig.colorbar(collection);