diff --git a/meshmode/discretization/connection/restriction.py b/meshmode/discretization/connection/restriction.py
new file mode 100644
index 000000000..390486e11
--- /dev/null
+++ b/meshmode/discretization/connection/restriction.py
@@ -0,0 +1,110 @@
+__copyright__ = "Copyright (C) 2022 University of Illinois Board of Trustees"
+
+__license__ = """
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
+"""
+
+
+from typing import Tuple
+import numpy as np
+
+from arraycontext import ArrayContext
+
+from meshmode.mesh import Mesh
+from meshmode.discretization import Discretization, ElementGroupBase
+from meshmode.discretization.connection.direct import (
+        DirectDiscretizationConnection, DiscretizationConnectionElementGroup,
+        InterpolationBatch)
+
+
+def _group_and_index_from_elements_indices(
+        discr: Discretization, element_indices: np.ndarray
+        ) -> Tuple[int, ElementGroupBase]:
+
+    from_group_index = 0
+    element_nr_base = 0
+    for igrp, grp in enumerate(discr.groups):
+        if np.array_equal(
+                np.arange(element_nr_base, element_nr_base+grp.nelements),
+                element_indices):
+            from_group_index = igrp
+
+    if from_group_index is None:
+        raise NotImplementedError("element_indices does not reflect an entire "
+                "element group. That's not supported at this point. Help welcome!")
+
+    return from_group_index, grp
+
+
+def make_volume_restriction(actx: ArrayContext, discr: Discretization,
+        element_indices: np.ndarray) -> DirectDiscretizationConnection:
+    """
+    :param element_indices: An array of integers indicating element numbers
+        to extract. Must be sorted in ascending order.
+
+    .. note::
+
+        Only supports extracting entire element groups for now.
+    """
+
+    # FIXME Generalize me to support arbitrary element subsets.
+
+    from_group_index, from_group = _group_and_index_from_elements_indices(
+            discr, element_indices)
+
+    submesh = Mesh(
+            vertices=discr.mesh.vertices,
+            groups=discr.mesh.groups[from_group_index:from_group_index+1],
+            vertex_id_dtype=discr.mesh.vertex_id_dtype,
+            element_id_dtype=discr.mesh.element_id_dtype,
+            is_conforming=discr.mesh.is_conforming)
+
+    subdiscr = Discretization(
+            actx, submesh, discr._group_factory,
+            real_dtype=discr.real_dtype)
+
+    conn_groups = [
+            DiscretizationConnectionElementGroup([
+                InterpolationBatch(
+                    from_group_index=from_group_index,
+                    from_element_indices=actx.freeze(actx.from_numpy(
+                        np.arange(from_group.nelements))),
+                    to_element_indices=actx.freeze(actx.from_numpy(
+                        np.arange(from_group.nelements))),
+                    result_unit_nodes=from_group.unit_nodes,
+                    to_element_face=None,
+                )])
+            ]
+    return DirectDiscretizationConnection(
+            discr, subdiscr, conn_groups,
+            is_surjective=False)
+
+
+def make_volume_embedding(actx: ArrayContext, discr: Discretization,
+        element_indices: np.ndarray) -> DirectDiscretizationConnection:
+    """
+    :param element_indices: An array of integers indicating element numbers
+        to extract. Must be sorted in ascending order.
+
+    .. note::
+
+        Only supports extracting entire element groups for now.
+    """
+
+# vim: foldmethod=marker