Nx larger

euler_error/diffusion_fixed_domain_euler_errors.py

@@ -44,8 +44,8 @@ def advection_diffusion(Nx, L, Nt, tmax, D):
     return c_array
 
 # parameters
-Nx, L, D, tmax = 32, 1, 0.1, 0.25
-nt_array = np.array([5, 10, 15, 20, 25, 50, 100, 200, 400, 800, 1600])
+Nx, L, D, tmax = 256, 1, 0.1, 0.25
+nt_array = np.array([2, 3, 4, 5, 10, 15, 20, 25, 50, 100, 200, 400, 800, 1600])
 dt_array = tmax/nt_array
 mesh = df.IntervalMesh(Nx, 0, L)
 x = mesh.coordinates()[:, 0]
@@ -63,7 +63,7 @@ for i in range(0, len(nt_array)):
     c = advection_diffusion(Nx, L, nt_array[i], tmax, D)
     error[i] = np.max(np.abs(c[-1] - c_exact[-1]))
 
-print('dt,t,error=', tmax/400, tmax, error[-3])
+print('dt,t,error=', tmax/800, tmax, error[-2])
 popt, pcov = curve_fit(linear_func, np.log(dt_array), np.log(error))
 print('The slope of the graph of log(error) vs log(dt) is', popt[0])
 fig, ax = plt.subplots(1)
@@ -72,3 +72,6 @@ ax.loglog(dt_array, error, 'bo')
 ax.set_xlabel('log(dt)')
 ax.set_ylabel('log(error)')
 plt.show()
+
+# |u_{exact} - u_{Nt}| < |u_{exact} - u_{Nx}| + |u_{Nx} - u_{Nt}| + floating point errors
+# to get the correct error in time, ensure first term small. That can be done by taking Nx large enough
\ No newline at end of file