import numpy as np
import matplotlib.pyplot as plt
import fealpy

# Specify parameters
num_spatial_divisions = 10
num_temporal_divisions = 100
adaptive_refinement_threshold = 0.001
adaptive_refinement_parameter = 0.5
adaptive_coarsening_parameter = 0.1

# Define the heat conduction equation model
model = fealpy.Poisson2DFEMModel()

# Generate initial mesh
mesh = fealpy.TriangleMesh()

# Define the Lagrange finite element space
space = fealpy.LagrangeFiniteElementSpace(mesh, p=1)

# Apply Dirichlet boundary conditions

# Solve the heat conduction equation using adaptive finite element method
while True:
    # Refine the mesh based on recovery estimate
    mesh.adaptive_refine(adaptive_refinement_threshold, recovery_type='residual')

    # Coarsen the mesh
    mesh.adaptive_coarsen(adaptive_coarsening_parameter)

    # Solve the heat conduction equation

    # Save plot of the mesh

    # Print error

    # Plot numerical solution at specified time steps

    # Check if error is below threshold
    if error < adaptive_refinement_threshold:
        break