diff --git a/amdis/VariadicGridFunctionOperator.hpp b/amdis/VariadicGridFunctionOperator.hpp
index 2271e1345f1d6a0ca7cc98c7e19cbc0cd80c1713..b505ded175ca605bfc9e88fc292d645930cec049 100644
--- a/amdis/VariadicGridFunctionOperator.hpp
+++ b/amdis/VariadicGridFunctionOperator.hpp
@@ -64,7 +64,7 @@ namespace AMDiS
     template <class GridView>
     void update(GridView const&) { /* do nothing */ }
 
-    ///\brief Turn this (global) Operator into a LocalOperator
+    /// \brief Turn this (global) Operator into a LocalOperator
     friend auto localOperator(VariadicGridFunctionOperator const& op)
     {
       return std::apply([&op](auto const& ... gfs){
@@ -92,7 +92,7 @@ namespace AMDiS
     -> VariadicGridFunctionOperator< Impl, GridFct... >;
 
 
-  /// \brief The main implementation of a LocalOperator depending on multiple LocalFunctions
+  /// \brief A LocalOperator parametrized by multiple LocalFunctions
   /**
    * A LocalOperator that takes multiple LocalFunctions as coefficient.
    * Provides quadrature rules and passes the LocalFunctions, bound to an element,
@@ -132,7 +132,7 @@ namespace AMDiS
 
     /// \brief Binds operator to `element`.
     /**
-     * By default, it binds the \ref localFct_ to the `element`.
+     * Binds all local functions in \ref localFct_ to the `element`.
      **/
     template <class Element>
     void bind(Element const& element)
@@ -210,6 +210,7 @@ namespace AMDiS
       }
     }
 
+    // get the polynomial order of a single local function or -1 if it cannot be determined.
     template<class LFF>
     constexpr int getOrder(LFF const& lf) const{
       if constexpr (Concepts::Polynomial<LFF>)
@@ -261,7 +262,7 @@ namespace AMDiS
 
 
   /** \brief Generator function for Operatorterms
-    * This is the user entry to the class. Any Local Operator implementation,
+    * This is the user entry to the class. Any Local Operator implementation
     * that has a corresponding specialization of the 'VariadicGridFunctionOperatorRegistry'
     * can be piped through this factory pattern.
     * \note compared to the single GridFunction 'makeOperator' here the order of arguments has changed!
@@ -279,7 +280,7 @@ namespace AMDiS
 #ifndef DOXYGEN
 
 
-  /// Generate an \ref VariadicGridFunctionOperator from a OperatorTerm (tag, expr).
+  /// Generate a \ref VariadicGridFunctionOperator from a corresponding OperatorTerm and a GridView.
   /// @{
   template <class Context, class Tag, class... Expr, class GridView>
   auto makeOperator(VariadicOperatorTerm<Tag,Expr...> const& op, GridView const& gridView)