diff --git a/sbp/Cargo.toml b/sbp/Cargo.toml
index 2fe2450..a84bb47 100644
--- a/sbp/Cargo.toml
+++ b/sbp/Cargo.toml
@@ -10,6 +10,11 @@ approx = "0.3.2"
 packed_simd = "0.3.3"
 json = "0.12.1"
 
+[features]
+# Internal feature flag to gate the expensive tests
+# which should be run only in release builds
+expensive_tests = []
+
 [dev-dependencies]
 criterion = "0.3.0"
 
diff --git a/sbp/src/euler.rs b/sbp/src/euler.rs
index 4370898..a9d2512 100644
--- a/sbp/src/euler.rs
+++ b/sbp/src/euler.rs
@@ -270,7 +270,8 @@ impl Field {
 }
 
 impl Field {
-    pub fn err_diff<SBP: SbpOperator>(&self, other: &Self) -> f32 {
+    /// sqrt((self-other)^T*H*(self-other))
+    pub fn h2_err<SBP: SbpOperator>(&self, other: &Self) -> f32 {
         assert_eq!(self.nx(), other.nx());
         assert_eq!(self.ny(), other.ny());
 
@@ -312,6 +313,7 @@ impl Field {
             .zip(other.0.iter())
             .map(|(((hx, hy), r0), r1)| (*r0 - *r1).powi(2) * hx * hy)
             .sum::<f32>()
+            .sqrt()
     }
 }
 
@@ -323,10 +325,10 @@ fn h2_diff() {
     }
     let field1 = Field::new(20, 21);
 
-    assert!((field0.err_diff::<super::operators::Upwind4>(&field1) - 4.0).abs() < 1e-3);
-    assert!((field0.err_diff::<super::operators::Upwind9>(&field1) - 4.0).abs() < 1e-3);
-    assert!((field0.err_diff::<super::operators::SBP4>(&field1) - 4.0).abs() < 1e-3);
-    assert!((field0.err_diff::<super::operators::SBP8>(&field1) - 4.0).abs() < 1e-3);
+    assert!((field0.h2_err::<super::operators::Upwind4>(&field1).powi(2) - 4.0).abs() < 1e-3);
+    assert!((field0.h2_err::<super::operators::Upwind9>(&field1).powi(2) - 4.0).abs() < 1e-3);
+    assert!((field0.h2_err::<super::operators::SBP4>(&field1).powi(2) - 4.0).abs() < 1e-3);
+    assert!((field0.h2_err::<super::operators::SBP8>(&field1).powi(2) - 4.0).abs() < 1e-3);
 }
 
 #[derive(Copy, Clone)]
diff --git a/sbp/tests/convergence.rs b/sbp/tests/convergence.rs
index 082b246..aee9f46 100644
--- a/sbp/tests/convergence.rs
+++ b/sbp/tests/convergence.rs
@@ -1,9 +1,10 @@
+#![cfg(feature = "expensive_tests")]
 use ndarray::prelude::*;
 use sbp::euler::*;
 
 fn run_with_size<SBP: sbp::operators::UpwindOperator>(size: usize) -> f32 {
-    let nx = 4 * size;
-    let ny = 4 * size;
+    let nx = size;
+    let ny = size;
     let x = Array1::linspace(-5.0, 5.0, nx);
     let y = Array1::linspace(-5.0, 5.0, ny);
 
@@ -26,7 +27,7 @@ fn run_with_size<SBP: sbp::operators::UpwindOperator>(size: usize) -> f32 {
     let mut sys = System::<SBP>::new(x, y);
     sys.vortex(0.0, vortex_params);
 
-    let time = 0.1;
+    let time = 0.2;
     let dt = 0.2 * f32::min(1.0 / (nx - 1) as f32, 1.0 / (ny - 1) as f32);
 
     let nsteps = (time / dt) as usize;
@@ -37,17 +38,30 @@ fn run_with_size<SBP: sbp::operators::UpwindOperator>(size: usize) -> f32 {
     let mut verifield = Field::new(ny, nx);
     verifield.vortex(sys.x(), sys.y(), nsteps as f32 * dt, vortex_params);
 
-    verifield.err_diff::<SBP>(sys.field())
+    verifield.h2_err::<SBP>(sys.field())
 }
 
 #[test]
-fn test() {
-    let sizes = [25, 35, 50, 71, 100];
-    let mut errs = Vec::with_capacity(sizes.len());
+fn convergence() {
+    let sizes = [25, 35, 50, 71, 100, 150];
+    let mut prev: Option<(usize, f32)> = None;
+    println!("Size\tError(h2)\tq");
     for size in &sizes {
-        println!("Size: {}", size);
-        let e = run_with_size::<sbp::operators::Upwind9>(*size);
-        errs.push(e);
+        print!("{:3}x{:3}", size, size);
+        let e = run_with_size::<sbp::operators::Upwind4>(*size);
+        print!("\t{:.10}", e);
+        if let Some(prev) = prev.take() {
+            let m0 = size * size;
+            let e0 = e;
+
+            let (size1, e1) = prev;
+            let m1 = size1 * size1;
+
+            let q = f32::log10(e0 / e1) / f32::log10((m0 as f32 / m1 as f32).powf(1.0 / 2.0));
+            print!("\t{}", q);
+        }
+        println!();
+        prev = Some((*size, e));
     }
-    panic!("{:?}", errs);
+    panic!();
 }