diff --git a/hog/forms.py b/hog/forms.py
index e8dc31b1c7c1926cfa900479aa5f3b0d52111645..8ae046393a7a8ad2b0330b12c960bb6eccfa7c1b 100644
--- a/hog/forms.py
+++ b/hog/forms.py
@@ -767,7 +767,6 @@ The resulting matrix must be multiplied with a vector of ones to be used as the
         docstring=docstring,
     )
 
-
 def divdiv(
     trial: TrialSpace,
     test: TestSpace,
@@ -813,6 +812,43 @@ Weak formulation
     )
 
 
+def k_divdiv(
+    trial: TrialSpace,
+    test: TestSpace,
+    geometry: ElementGeometry,
+    symbolizer: Symbolizer,
+    coefficient_function_space: Optional[FunctionSpace] = None,
+    blending: GeometryMap = IdentityMap(),
+) -> Form:
+    docstring = f"""
+divdiv operator which is the compressible part of full Stokes operator
+
+Geometry map:    {blending}
+
+Weak formulation
+
+    u: trial function (vectorial space: {trial})
+    v: test function  (vectorial space: {test})
+
+    ∫ μ ( ∇ · u ) · ( ∇ · v )
+"""
+
+    from hog.recipes.integrands.volume.divdiv import integrand
+
+    return process_integrand(
+        integrand,
+        trial,
+        test,
+        geometry,
+        symbolizer,
+        blending=blending,
+        is_symmetric=trial == test,
+        docstring=docstring,
+        fe_coefficients={
+            "k": coefficient_function_space
+        }
+    )
+
 def advection(
     trial: TrialSpace,
     test: TestSpace,
diff --git a/hog/recipes/integrands/volume/divdiv.py b/hog/recipes/integrands/volume/divdiv.py
index 80315d110b8eb18e74902c1f20009b27c6ca4f72..5a417a617fc132e47dfac2f416611bd6d2cf3c0f 100644
--- a/hog/recipes/integrands/volume/divdiv.py
+++ b/hog/recipes/integrands/volume/divdiv.py
@@ -26,8 +26,9 @@ def integrand(
     grad_u,
     grad_v,
     tabulate,
+    k,
     **_,
 ):
     div_u = (jac_b_inv.T * tabulate(jac_a_inv.T * grad_u)).trace()
     div_v = (jac_b_inv.T * tabulate(jac_a_inv.T * grad_v)).trace()
-    return div_u * div_v * tabulate(jac_a_abs_det) * jac_b_abs_det
+    return (k["k"] if "k" in k else 1.0) * div_u * div_v * tabulate(jac_a_abs_det) * jac_b_abs_det