Allow coincident nodes on mortar boundaries

Closes idaholab#21680

framework/src/constraints/AutomaticMortarGeneration.C

@@ -1850,10 +1850,13 @@ AutomaticMortarGeneration::projectSecondaryNodesSinglePair(
                                                                          secondary_val);
                   }
 
-              // Sanity check
               if (!found_match)
-                mooseError("Could not associate primary/secondary neighbors on either side of "
-                           "secondary_node.");
+              {
+                // There could be coincident nodes and this might be a bad primary candidate (see
+                // issue #21680). Instead of giving up, let's try continuing
+                rejected_primary_elem_candidates.insert(primary_elem_candidate);
+                continue;
+              }
 
               // We need to handle the case where we've exactly projected a secondary node onto a
               // primary node, but our secondary node is at one of the secondary face endpoints and
@@ -1894,10 +1897,8 @@ AutomaticMortarGeneration::projectSecondaryNodesSinglePair(
             break; // out of e-loop
           }
           else
-          {
             // The current secondary_node is not in this Elem, so keep track of the rejects.
             rejected_primary_elem_candidates.insert(primary_elem_candidate);
-          }
         }
 
         if (projection_succeeded)

test/tests/mortar/coincident-nodes/test.i

@@ -0,0 +1,63 @@
+[Mesh]
+  [top]
+    type = GeneratedMeshGenerator
+    dim = 2
+    ymin = 0.5
+    ymax = 1
+    nx = 2
+    ny = 1
+    subdomain_ids = '0 0'
+  []
+  [bottom]
+    type = GeneratedMeshGenerator
+    dim = 2
+    ymin = 0
+    ymax = 0.5
+    nx = 2
+    ny = 1
+    subdomain_ids = '1 1'
+  []
+  [combine]
+    type = CombinerGenerator
+    inputs = 'top bottom'
+  []
+  [secondary]
+    type = LowerDBlockFromSidesetGenerator
+    input = combine
+    sidesets = left
+    new_block_id = 11
+    new_block_name = secondary
+  []
+  [primary]
+    type = LowerDBlockFromSidesetGenerator
+    input = secondary
+    sidesets = right
+    new_block_id = 12
+    new_block_name = primary
+  []
+[]
+
+[Problem]
+  solve = false
+[]
+
+[Variables]
+  [u][]
+[]
+
+[Constraints]
+  [mortar]
+    type = PenaltyEqualValueConstraint
+    secondary_variable = u
+    primary_boundary = right
+    secondary_boundary = left
+    primary_subdomain = 12
+    secondary_subdomain = 11
+    penalty_value = 10
+  []
+[]
+
+[Executioner]
+  type = Transient
+  num_steps = 1
+[]

test/tests/mortar/coincident-nodes/tests

@@ -0,0 +1,9 @@
+[Tests]
+  [coincident]
+    type = RunApp
+    input = test.i
+    requirement = 'The system shall be able to construct a mortar mesh when coincident nodes exist on one or more mortar boundaries.'
+    design = 'Constraints/index.md'
+    issues = '#21680'
+  []
+[]