diff --git a/meshmode/discretization/connection/__init__.py b/meshmode/discretization/connection/__init__.py
index dcfcd5e318eeba84551806d817f4631e85fb042e..fcb6cc6983bc1d08cb8e2878ccc5b748c3e4b573 100644
--- a/meshmode/discretization/connection/__init__.py
+++ b/meshmode/discretization/connection/__init__.py
@@ -164,13 +164,18 @@ class DiscretizationConnection(object):
         instances, with a one-to-one correspondence to the groups in
         :attr:`to_discr`.
 
+    .. attribute:: is_surjective
+
+        A :class:`bool` indicating whether every output degree
+        of freedom is set by the connection.
+
     .. automethod:: __call__
 
     .. automethod:: full_resample_matrix
 
     """
 
-    def __init__(self, from_discr, to_discr, groups):
+    def __init__(self, from_discr, to_discr, groups, is_surjective):
         if from_discr.cl_context != to_discr.cl_context:
             raise ValueError("from_discr and to_discr must live in the "
                     "same OpenCL context")
@@ -191,6 +196,8 @@ class DiscretizationConnection(object):
         self.to_discr = to_discr
         self.groups = groups
 
+        self.is_surjective = is_surjective
+
     @memoize_method
     def _resample_matrix(self, to_group_index, ibatch_index):
         import modepy as mp
@@ -356,7 +363,10 @@ class DiscretizationConnection(object):
         if not isinstance(vec, cl.array.Array):
             return vec
 
-        result = self.to_discr.empty(dtype=vec.dtype)
+        if self.is_surjective:
+            result = self.to_discr.empty(dtype=vec.dtype)
+        else:
+            result = self.to_discr.zeros(dtype=vec.dtype)
 
         if vec.shape != (self.from_discr.nnodes,):
             raise ValueError("invalid shape of incoming resampling data")
diff --git a/meshmode/discretization/connection/face.py b/meshmode/discretization/connection/face.py
index f847e5dae9ebce17049b82de5e90d6d68dac9234..521dd0561a2d707ce53f6ca43d50a7ce36dffb2f 100644
--- a/meshmode/discretization/connection/face.py
+++ b/meshmode/discretization/connection/face.py
@@ -81,7 +81,8 @@ def _build_boundary_connection(queue, vol_discr, bdry_discr, connection_data):
                     connection_batches))
 
     return DiscretizationConnection(
-            vol_discr, bdry_discr, connection_groups)
+            vol_discr, bdry_discr, connection_groups,
+            is_surjective=True)
 
 # }}}
 
diff --git a/meshmode/discretization/connection/opposite_face.py b/meshmode/discretization/connection/opposite_face.py
index 7c0cef52e2adb8356cbc00c7a0c97eaeb19e16c8..b7b92aba9b3ce242e81ddb9e3beef1b882f1cb1b 100644
--- a/meshmode/discretization/connection/opposite_face.py
+++ b/meshmode/discretization/connection/opposite_face.py
@@ -383,7 +383,8 @@ def make_opposite_face_connection(volume_to_bdry_conn):
             to_discr=bdry_discr,
             groups=[
                 DiscretizationConnectionElementGroup(batches=batches)
-                for batches in groups])
+                for batches in groups],
+            is_surjective=True)
 
 # }}}
 
diff --git a/meshmode/discretization/connection/same_mesh.py b/meshmode/discretization/connection/same_mesh.py
index 7f07f5988cedca0bff0986627c935bbf37f74593..3b73e34fefd5115e01b97728ab414cc8c77fd178 100644
--- a/meshmode/discretization/connection/same_mesh.py
+++ b/meshmode/discretization/connection/same_mesh.py
@@ -57,7 +57,8 @@ def make_same_mesh_connection(to_discr, from_discr):
                     DiscretizationConnectionElementGroup([ibatch]))
 
     return DiscretizationConnection(
-            from_discr, to_discr, groups)
+            from_discr, to_discr, groups,
+            is_surjective=True)
 
 # }}}