diff --git a/include/aspect/material_model/utilities.h b/include/aspect/material_model/utilities.h
index c9923e61ee3..4a50205a694 100644
--- a/include/aspect/material_model/utilities.h
+++ b/include/aspect/material_model/utilities.h
@@ -570,8 +570,9 @@ namespace aspect
 
           /**
            * Percentage of material that has already undergone the phase
-           * transition to the higher-pressure material (this is done
-           * individually for each transition and summed up in the end)
+           * transition to the higher-pressure material. For this class
+           * this function only returns 1.0 or 0.0, depending on whether
+           * the selected phase transition has been crossed or not.
            */
           double compute_value (const PhaseFunctionInputs<dim> &in) const;
 
@@ -579,7 +580,7 @@ namespace aspect
            * Return the derivative of the phase function with respect to
            * pressure.
            */
-          double compute_derivative (const PhaseFunctionInputs<dim> &in) const;
+          double compute_derivative () const;
 
           /**
            * Return the total number of phase transitions.
diff --git a/include/aspect/material_model/visco_plastic.h b/include/aspect/material_model/visco_plastic.h
index 7f4ec6dc055..75914d27b7c 100644
--- a/include/aspect/material_model/visco_plastic.h
+++ b/include/aspect/material_model/visco_plastic.h
@@ -273,7 +273,7 @@ namespace aspect
         bool use_dominant_phase_for_viscosity;
 
         /**
-         * Object that handles phase transitions.
+         * Object that handles discrete phase transitions for the rheology if requested by the variable use_dominant_phase_for_viscosity.
          */
         MaterialUtilities::PhaseFunctionDiscrete<dim> phase_function_discrete;
 
diff --git a/include/aspect/structured_data.h b/include/aspect/structured_data.h
index 97455b6fa46..341a871187a 100644
--- a/include/aspect/structured_data.h
+++ b/include/aspect/structured_data.h
@@ -249,12 +249,13 @@ namespace aspect
         double get_maximum_component_value(const unsigned int component) const;
 
         /**
-        Retrieve the number of table points for a given dimension.
-        Equivalent to calling get_interpolation_point_coordinates().size().
-        @param dimension The index of the dimension for which to get the number of table points.
-        @return The number of points along the specified dimension.
-        */
-        unsigned get_number_of_coordinates(const unsigned int dimension) const;
+         * Retrieve the number of table points for a given dimension.
+         * Equivalent to calling get_interpolation_point_coordinates().size().
+         *
+         * @param dimension The index of the dimension for which to get the number of table points.
+         * @return The number of points along the specified dimension.
+         */
+        unsigned int get_number_of_coordinates(const unsigned int dimension) const;
 
       private:
         /**
diff --git a/source/material_model/utilities.cc b/source/material_model/utilities.cc
index da5e0b581f4..03da889b0b9 100644
--- a/source/material_model/utilities.cc
+++ b/source/material_model/utilities.cc
@@ -1181,7 +1181,7 @@ namespace aspect
             material_lookup[i]->load_file(data_directory+material_file_names[i],
                                           this->get_mpi_communicator());
 
-            assert(material_lookup[i]->has_equidistant_coordinates());
+            Assert(material_lookup[i]->has_equidistant_coordinates(), ExcMessage("The loaded lookup tables do not use equidistant coordinates. The class 'PhaseFunctionDiscrete' cannot currently handle non equidistant coordinates."));
 
             minimum_temperature[i] = material_lookup[i]->get_interpolation_point_coordinates(0).front();
             maximum_temperature[i] = material_lookup[i]->get_interpolation_point_coordinates(0).back();
@@ -1254,7 +1254,7 @@ namespace aspect
 
       template <int dim>
       double
-      PhaseFunctionDiscrete<dim>::compute_derivative (const PhaseFunctionInputs<dim> &in) const
+      PhaseFunctionDiscrete<dim>::compute_derivative () const
       {
         // make sure the phase derivative of this phase function is not asked for.
         AssertThrow(false, ExcNotImplemented());
@@ -1348,7 +1348,7 @@ namespace aspect
                            "The file names of the material data (material "
                            "data is assumed to be in order with the ordering "
                            "of the compositional fields). Note that there are "
-                           "three options on how many files need to be listed "
+                           "two options on how many files need to be listed "
                            "here: 1. If only one file is provided, it is used "
                            "for the whole model domain, and compositional fields "
                            "are ignored. 2. If there is one more file name than the "