def SolveHeatProblem(f, g, u0, alpha, V, solution, flag):
    T=1
    num_steps=200
    t = 0
    dt  = 0.1*T / num_steps
    mesh, triangulation = CreateUnitCircleMesh()
    t = 0
    V = FunctionSpace(mesh,'P',1)
    u_now = interpolate(u0,V)
    for i in range(num_steps):
        t+=dt
        if hasattr(f,"t"):
            f.t = t
        if hasattr(g,"t"):
            g.t = t
        f_np1 = (1/alpha)*interpolate(f,V) + u_now/(alpha*dt)
        u_now = SolveHelmholtz(f_np1, g, 1/(dt), mesh, V, flag)
        if hasattr(solution,"t"):
            solution.t=t
            errC,errL2 = compute_errors(u,solution,mesh)
            print("Step: "+str(i))
            print("C norm error = "+str(errC))
            print("L2 norm error = "+str(errL2))
    return u_now

#2.2.2
u=SolveHeatProblem(Expression("(x[0]*x[0]+x[1]*x[1])-4*(t-0.025)",degree=3,t=0),Expression("2*t",degree=1,t=0),
        Expression('0',degree=0),3,mesh,Expression("(x[0]*x[0]+x[1]*x[1])*t",degree=3,t=0),flag=2)
print("Dirichlet problem for the Heatequation.")
print("C error = "+str(errC))
print("L2 error = "+str(errL2))