diff --git a/src/nomad_simulations/schema_packages/basis_set.py b/src/nomad_simulations/schema_packages/basis_set.py
index 4aaf55f6..0428c0c6 100644
--- a/src/nomad_simulations/schema_packages/basis_set.py
+++ b/src/nomad_simulations/schema_packages/basis_set.py
@@ -247,11 +247,14 @@ def normalize(self, archive: 'EntryArchive', logger: 'BoundLogger') -> None:
         if self.n_primitive is not None:
             if self.exponents is not None and len(self.exponents) != self.n_primitive:
                 raise ValueError(
-                f"Mismatch in number of exponents: expected {self.n_primitive}, found {len(self.exponents)}."
+                    f'Mismatch in number of exponents: expected {self.n_primitive}, found {len(self.exponents)}.'
                 )
-            if self.contraction_coefficients is not None and len(self.contraction_coefficients) != self.n_primitive:
+            if (
+                self.contraction_coefficients is not None
+                and len(self.contraction_coefficients) != self.n_primitive
+            ):
                 raise ValueError(
-                f"Mismatch in number of contraction coefficients: expected {self.n_primitive}, found {len(self.contraction_coefficients)}."
+                    f'Mismatch in number of contraction coefficients: expected {self.n_primitive}, found {len(self.contraction_coefficients)}.'
                 )
 
 
diff --git a/src/nomad_simulations/schema_packages/numerical_settings.py b/src/nomad_simulations/schema_packages/numerical_settings.py
index 63fb2ab4..37842f84 100644
--- a/src/nomad_simulations/schema_packages/numerical_settings.py
+++ b/src/nomad_simulations/schema_packages/numerical_settings.py
@@ -202,6 +202,12 @@ class NumericalIntegration(NumericalSettings):
 
     def normalize(self, archive: 'EntryArchive', logger: 'BoundLogger') -> None:
         super().normalize(archive, logger)
+        valid_coordinates = ['full', 'radial', 'angular', None]
+        if self.coordinate not in valid_coordinates:
+            logger.warning(
+                f'Invalid coordinate value: {self.coordinate}. Resetting to None.'
+            )
+            self.coordinate = None
 
 
 class KSpaceFunctionalities:
diff --git a/tests/test_basis_set.py b/tests/test_basis_set.py
index e96c224b..eb2e20f0 100644
--- a/tests/test_basis_set.py
+++ b/tests/test_basis_set.py
@@ -500,6 +500,7 @@ def test_atom_centered_basis_set_normalize() -> None:
     # Add checks for normalized behavior, if any
     assert bs.basis_set == 'cc-pVTZ'
 
+
 def test_atom_centered_basis_set_invalid_data() -> None:
     """Test behavior with missing or invalid data."""
     bs = AtomCenteredBasisSet(
@@ -522,8 +523,5 @@ def test_atom_centered_basis_set_invalid_data() -> None:
     bs.functional_composition = [invalid_function]
 
     # Call normalize to trigger validation
-    with pytest.raises(ValueError, match="Mismatch in number of exponents"):
+    with pytest.raises(ValueError, match='Mismatch in number of exponents'):
         invalid_function.normalize(None, logger)
-
-
-
diff --git a/tests/test_numerical_settings.py b/tests/test_numerical_settings.py
index 6426b4cd..0ead803f 100644
--- a/tests/test_numerical_settings.py
+++ b/tests/test_numerical_settings.py
@@ -9,6 +9,8 @@
     KLinePath,
     KMesh,
     KSpaceFunctionalities,
+    Mesh,
+    NumericalIntegration,
 )
 
 from . import logger
@@ -377,3 +379,82 @@ def test_resolve_points(self, k_line_path: KLinePath):
             ]
         )
         assert np.allclose(k_line_path.points, points)
+
+
+@pytest.mark.parametrize(
+    'dimensionality, expected_warning',
+    [
+        (3, None),  # Valid case
+        (2, None),  # Valid case
+        (
+            5,
+            '`dimensionality` meshes different than 1, 2, or 3 are not supported.',
+        ),  # Invalid
+        (
+            0,
+            '`dimensionality` meshes different than 1, 2, or 3 are not supported.',
+        ),  # Invalid
+    ],
+)
+def test_mesh_dimensionality_validation(dimensionality, expected_warning, caplog):
+    mesh = Mesh(dimensionality=dimensionality)
+    mesh.normalize(None, logger)
+    if expected_warning:
+        assert expected_warning in caplog.text
+    else:
+        assert caplog.text == ''
+
+
+@pytest.mark.parametrize(
+    'dimensionality, grid, points',
+    [
+        (3, [10, 10, 10], None),  # Valid grid, no points defined yet
+        (3, None, None),  # Missing grid and points
+        (
+            3,
+            [10, 10, 10],
+            [[0, 0, 0], [1, 1, 1]],
+        ),  # Valid points (though fewer than grid suggests)
+    ],
+)
+def test_mesh_grid_and_points(dimensionality, grid, points):
+    mesh = Mesh(dimensionality=dimensionality, grid=grid, points=points)
+    assert mesh.dimensionality == dimensionality
+    if grid is not None:
+        assert np.allclose(mesh.grid, grid)
+    else:
+        assert mesh.grid == grid
+    if points is not None:
+        assert np.allclose(mesh.points, points)
+    else:
+        assert mesh.points == points
+
+
+def test_mesh_spacing_normalization():
+    mesh = Mesh(dimensionality=3, grid=[10, 10, 10], spacing=[0.1, 0.1, 0.1])
+    mesh.normalize(None, logger)
+    assert np.allclose(mesh.spacing, [0.1, 0.1, 0.1])
+
+
+def test_numerical_integration_mesh():
+    mesh = Mesh(dimensionality=3, grid=[10, 10, 10])
+    integration = NumericalIntegration(mesh=mesh)
+    assert integration.mesh.dimensionality == 3
+    assert np.allclose(integration.mesh.grid, [10, 10, 10])
+
+
+@pytest.mark.parametrize(
+    'integration_thresh, weight_cutoff',
+    [
+        (1e-6, 1e-3),  # Valid thresholds
+        (None, 1e-3),  # Missing integration threshold
+        (1e-6, None),  # Missing weight cutoff
+        (None, None),  # Both thresholds missing
+    ],
+)
+def test_numerical_integration_thresholds(integration_thresh, weight_cutoff):
+    integration = NumericalIntegration(
+        integration_thresh=integration_thresh, weight_cutoff=weight_cutoff
+    )
+    assert integration.integration_thresh == integration_thresh
+    assert integration.weight_cutoff == weight_cutoff