diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 9b3751407b..3dd3b7f413 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -9,4 +9,30 @@ abstract type AbstractSemidiscretization end
 abstract type AbstractEquations{NDIMS, NVARS} end
 
 
+# abstract supertype of specific SBP bases such as a Lobatto-Legendre nodal basis
+abstract type AbstractBasisSBP{RealT<:Real} end
+
+
+# abstract supertype of mortar methods, e.g. using L² projections
+abstract type AbstractMortar{RealT<:Real} end
+
+# abstract supertype of mortar methods using L² projection
+# which will be specialized for different SBP bases
+abstract type MortarL2{RealT<:Real} <: AbstractMortar{RealT} end
+
+
+# abstract supertype of functionality related to the analysis of
+# numerical solutions, e.g. the calculation of errors
+abstract type SolutionAnalyzer{RealT<:Real} end
+
+
+# abstract supertype of grid-transfer methods used for AMR,
+# e.g. refinement and coarsening based on L² projections
+abstract type AdaptorAMR{RealT<:Real} end
+
+# abstract supertype of AMR grid-transfer operations using L² projections
+# which will be specialized for different SBP bases
+abstract type AdaptorL2{RealT<:Real} <: AdaptorAMR{RealT} end
+
+
 # TODO: Taal decide, which abstract types shall be defined here?
diff --git a/src/solvers/dg/lobatto_legendre.jl b/src/solvers/dg/basis_lobatto_legendre.jl
similarity index 100%
rename from src/solvers/dg/lobatto_legendre.jl
rename to src/solvers/dg/basis_lobatto_legendre.jl
diff --git a/src/solvers/dg/dg.jl b/src/solvers/dg/dg.jl
index 39a2481e4c..1a2b938ac8 100644
--- a/src/solvers/dg/dg.jl
+++ b/src/solvers/dg/dg.jl
@@ -129,13 +129,12 @@ end
 
 
 
-abstract type AbstractBasisSBP{RealT<:Real} end
-
-abstract type AbstractMortar{RealT<:Real} end
-
-abstract type MortarL2{RealT<:Real} <: AbstractMortar{RealT} end
-
+"""
+    DG(basis, basis, surface_flux, volume_integral)
 
+Create a discontinuous Galerkin method.
+If `basis isa LobattoLegendreBasis`, this creates a [`DGSEM`](@ref).
+"""
 struct DG{RealT, Basis<:AbstractBasisSBP{RealT}, Mortar, SurfaceFlux, VolumeIntegral}
   basis::Basis
   mortar::Mortar
@@ -226,12 +225,6 @@ end
 
 
 # Used for analyze_solution
-abstract type SolutionAnalyzer{RealT<:Real} end
-
-abstract type AdaptorAMR{RealT<:Real} end
-
-abstract type AdaptorL2{RealT<:Real} <: AdaptorAMR{RealT} end
-
 SolutionAnalyzer(dg::DG; kwargs...) = SolutionAnalyzer(dg.basis; kwargs...)
 
 AdaptorAMR(mesh, dg::DG) = AdaptorL2(dg.basis)
@@ -241,7 +234,7 @@ AdaptorAMR(mesh, dg::DG) = AdaptorL2(dg.basis)
 # Include utilities
 include("interpolation.jl")
 include("l2projection.jl")
-include("lobatto_legendre.jl")
+include("basis_lobatto_legendre.jl")
 
 """
     DGSEM([RealT=Float64,] polydeg::Integer,