diff --git a/src/navier-stokes.c b/src/navier-stokes.c
index 3471ab9..186864e 100644
--- a/src/navier-stokes.c
+++ b/src/navier-stokes.c
@@ -22,6 +22,8 @@ limitations under the License.
 #include <stdlib.h>
 #include <string.h>
 
+#define CABS2(x) ((__real__ x) * (__real__ x) + (__imag__ x) * (__imag__ x))
+
 // compute solution as a function of time
 int uk(
   int K1,
@@ -943,9 +945,9 @@ int ns_step_rkdp54(
   for(kx=0;kx<=K1;kx++){
     for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
       // difference between 5th order and 4th order
-      // use the norm |u_i|/k^3
-      err+=cabs((*delta)*(-71./57600*(*k1)[klookup_sym(kx,ky,K2)]+71./16695*k3[klookup_sym(kx,ky,K2)]-71./1920*k4[klookup_sym(kx,ky,K2)]+17253./339200*k5[klookup_sym(kx,ky,K2)]-22./525*k6[klookup_sym(kx,ky,K2)]+1./40*(*k2)[klookup_sym(kx,ky,K2)]))/pow(kx*kx+ky*ky,1.5);
-      relative+=cabs(tmp[klookup_sym(kx,ky,K2)]-u[klookup_sym(kx,ky,K2)])/pow(kx*kx+ky*ky,1.5);
+      // use the norm |u_k|^2k^2 (to get a bound on the error of the enstrophy)
+      err+=(kx*kx+ky*ky)*CABS2((*delta)*(-71./57600*(*k1)[klookup_sym(kx,ky,K2)]+71./16695*k3[klookup_sym(kx,ky,K2)]-71./1920*k4[klookup_sym(kx,ky,K2)]+17253./339200*k5[klookup_sym(kx,ky,K2)]-22./525*k6[klookup_sym(kx,ky,K2)]+1./40*(*k2)[klookup_sym(kx,ky,K2)]));
+      relative+=(kx*kx+ky*ky)*(CABS2(tmp[klookup_sym(kx,ky,K2)]-u[klookup_sym(kx,ky,K2)]));
     }
   }