from fealpy import *
import matplotlib.pyplot as plt

# Specify parameters
num_spatial_divisions = 10
num_temporal_divisions = 100
adaptive_refinement_stop_threshold = 1e-6
adaptive_refinement_parameter = 0.5
adaptive_coarsening_parameter = 0.5

# Create mesh
mesh = TriangleMesh()

# Define finite element space
space = LagrangeFiniteElementSpace(mesh, p=1)

# Define initial condition
u0 = space.function()
u0[:] = 0.0

# Define Dirichlet boundary conditions
def dirichlet_bc(x, on_boundary):
    return on_boundary

# Solve heat conduction equation using adaptive finite element method
for step in range(num_temporal_divisions):
    # Refine mesh adaptively
    adaptive_refine(mesh, space, u0, stop_threshold=adaptive_refinement_stop_threshold, parameter=adaptive_refinement_parameter)
    
    # Solve for the current time step
    u1 = space.function()
    u1[:] = 0.0
    # Code to solve for u1
    
    # Coarsen mesh
    adaptive_coarsen(mesh, space, u1, parameter=adaptive_coarsening_parameter)
    
    # Update u0 for next time step
    u0[:] = u1
    
    # Save plot of mesh
    plt.figure()
    mesh.add_plot(plt)
    plt.savefig(f"mesh_step_{step}.png")
    plt.close()
    
    # Print error
    error = 0.0
    print(f"Error at time step {step}: {error}")
    
    # Plot numerical solution at specified time steps
    if step % 10 == 0:
        plt.figure()
        space.add_plot(plt, u1)
        plt.savefig(f"numerical_solution_step_{step}.png")
        plt.close()