#!/usr/bin/env python
# coding: utf-8

# # 2D FEM using Firedrake
# 
# Copyright (C) 2026 Andreas Kloeckner
# 
# <details>
# <summary>MIT License</summary>
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# 
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
# 
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
# </details>
# 

# 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)


# 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


# 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)


# In[24]:


fig = plt.figure(figsize=(10, 10))
axes = fig.add_subplot(111, projection='3d')
trisurf(U, axes=axes)


# In[ ]: