diff --git a/src/solvers/dgsem_tree/dg.jl b/src/solvers/dgsem_tree/dg.jl
index febfb0b121f..fd9728168d8 100644
--- a/src/solvers/dgsem_tree/dg.jl
+++ b/src/solvers/dgsem_tree/dg.jl
@@ -15,33 +15,6 @@ function reset_du!(du, dg, cache)
     return du
 end
 
-#     pure_and_blended_element_ids!(element_ids_dg, element_ids_dgfv, alpha, dg, cache)
-#
-# Given blending factors `alpha` and the solver `dg`, fill
-# `element_ids_dg` with the IDs of elements using a pure DG scheme and
-# `element_ids_dgfv` with the IDs of elements using a blended DG-FV scheme.
-function pure_and_blended_element_ids!(element_ids_dg, element_ids_dgfv, alpha, dg::DG,
-                                       cache)
-    empty!(element_ids_dg)
-    empty!(element_ids_dgfv)
-    # For `Float64`, this gives 1.8189894035458565e-12
-    # For `Float32`, this gives 1.1920929f-5
-    RealT = eltype(alpha)
-    atol = max(100 * eps(RealT), eps(RealT)^convert(RealT, 0.75f0))
-
-    for element in eachelement(dg, cache)
-        # Clip blending factor for values close to zero (-> pure DG)
-        dg_only = isapprox(alpha[element], 0, atol = atol)
-        if dg_only
-            push!(element_ids_dg, element)
-        else
-            push!(element_ids_dgfv, element)
-        end
-    end
-
-    return nothing
-end
-
 function volume_jacobian(element, mesh::TreeMesh, cache)
     return inv(cache.elements.inverse_jacobian[element])^ndims(mesh)
 end
diff --git a/src/solvers/dgsem_tree/dg_1d.jl b/src/solvers/dgsem_tree/dg_1d.jl
index d9a8cc8bc6d..4b449a259d7 100644
--- a/src/solvers/dgsem_tree/dg_1d.jl
+++ b/src/solvers/dgsem_tree/dg_1d.jl
@@ -42,9 +42,6 @@ end
 function create_cache(mesh::Union{TreeMesh{1}, StructuredMesh{1}, P4estMesh{1}},
                       equations,
                       volume_integral::VolumeIntegralShockCapturingHG, dg::DG, uEltype)
-    element_ids_dg = Int[]
-    element_ids_dgfv = Int[]
-
     cache = create_cache(mesh, equations,
                          VolumeIntegralFluxDifferencing(volume_integral.volume_flux_dg),
                          dg, uEltype)
@@ -55,8 +52,7 @@ function create_cache(mesh::Union{TreeMesh{1}, StructuredMesh{1}, P4estMesh{1}},
     fstar1_R_threaded = A2dp1_x[A2dp1_x(undef, nvariables(equations), nnodes(dg) + 1)
                                 for _ in 1:Threads.nthreads()]
 
-    return (; cache..., element_ids_dg, element_ids_dgfv, fstar1_L_threaded,
-            fstar1_R_threaded)
+    return (; cache..., fstar1_L_threaded, fstar1_R_threaded)
 end
 
 function create_cache(mesh::Union{TreeMesh{1}, StructuredMesh{1}, P4estMesh{1}},
@@ -256,37 +252,33 @@ function calc_volume_integral!(du, u,
                                nonconservative_terms, equations,
                                volume_integral::VolumeIntegralShockCapturingHG,
                                dg::DGSEM, cache)
-    @unpack element_ids_dg, element_ids_dgfv = cache
     @unpack volume_flux_dg, volume_flux_fv, indicator = volume_integral
 
     # Calculate blending factors α: u = u_DG * (1 - α) + u_FV * α
     alpha = @trixi_timeit timer() "blending factors" indicator(u, mesh, equations, dg,
                                                                cache)
 
-    # Determine element ids for DG-only and blended DG-FV volume integral
-    pure_and_blended_element_ids!(element_ids_dg, element_ids_dgfv, alpha, dg, cache)
-
-    # Loop over pure DG elements
-    @trixi_timeit timer() "pure DG" @threaded for idx_element in eachindex(element_ids_dg)
-        element = element_ids_dg[idx_element]
-        flux_differencing_kernel!(du, u, element, mesh, nonconservative_terms,
-                                  equations,
-                                  volume_flux_dg, dg, cache)
-    end
-
-    # Loop over blended DG-FV elements
-    @trixi_timeit timer() "blended DG-FV" @threaded for idx_element in eachindex(element_ids_dgfv)
-        element = element_ids_dgfv[idx_element]
+    RealT = eltype(alpha)
+    atol = max(100 * eps(RealT), eps(RealT)^convert(RealT, 0.75f0))
+    @threaded for element in eachelement(dg, cache)
         alpha_element = alpha[element]
-
-        # Calculate DG volume integral contribution
-        flux_differencing_kernel!(du, u, element, mesh, nonconservative_terms,
-                                  equations,
-                                  volume_flux_dg, dg, cache, 1 - alpha_element)
-
-        # Calculate FV volume integral contribution
-        fv_kernel!(du, u, mesh, nonconservative_terms, equations, volume_flux_fv,
-                   dg, cache, element, alpha_element)
+        # Clip blending factor for values close to zero (-> pure DG)
+        dg_only = isapprox(alpha_element, 0, atol = atol)
+
+        if dg_only
+            flux_differencing_kernel!(du, u, element, mesh,
+                                      nonconservative_terms, equations,
+                                      volume_flux_dg, dg, cache)
+        else
+            # Calculate DG volume integral contribution
+            flux_differencing_kernel!(du, u, element, mesh,
+                                      nonconservative_terms, equations,
+                                      volume_flux_dg, dg, cache, 1 - alpha_element)
+
+            # Calculate FV volume integral contribution
+            fv_kernel!(du, u, mesh, nonconservative_terms, equations, volume_flux_fv,
+                       dg, cache, element, alpha_element)
+        end
     end
 
     return nothing
diff --git a/src/solvers/dgsem_tree/dg_3d.jl b/src/solvers/dgsem_tree/dg_3d.jl
index 85150bc3040..1e8c305edeb 100644
--- a/src/solvers/dgsem_tree/dg_3d.jl
+++ b/src/solvers/dgsem_tree/dg_3d.jl
@@ -47,9 +47,6 @@ function create_cache(mesh::Union{TreeMesh{3}, StructuredMesh{3}, P4estMesh{3},
                                   T8codeMesh{3}},
                       equations,
                       volume_integral::VolumeIntegralShockCapturingHG, dg::DG, uEltype)
-    element_ids_dg = Int[]
-    element_ids_dgfv = Int[]
-
     cache = create_cache(mesh, equations,
                          VolumeIntegralFluxDifferencing(volume_integral.volume_flux_dg),
                          dg, uEltype)
@@ -76,8 +73,7 @@ function create_cache(mesh::Union{TreeMesh{3}, StructuredMesh{3}, P4estMesh{3},
                                         nnodes(dg), nnodes(dg) + 1)
                                 for _ in 1:Threads.nthreads()]
 
-    return (; cache..., element_ids_dg, element_ids_dgfv, fstar1_L_threaded,
-            fstar1_R_threaded,
+    return (; cache..., fstar1_L_threaded, fstar1_R_threaded,
             fstar2_L_threaded, fstar2_R_threaded, fstar3_L_threaded, fstar3_R_threaded)
 end
 
@@ -386,37 +382,33 @@ function calc_volume_integral!(du, u,
                                nonconservative_terms, equations,
                                volume_integral::VolumeIntegralShockCapturingHG,
                                dg::DGSEM, cache)
-    @unpack element_ids_dg, element_ids_dgfv = cache
     @unpack volume_flux_dg, volume_flux_fv, indicator = volume_integral
 
     # Calculate blending factors α: u = u_DG * (1 - α) + u_FV * α
     alpha = @trixi_timeit timer() "blending factors" indicator(u, mesh, equations, dg,
                                                                cache)
 
-    # Determine element ids for DG-only and blended DG-FV volume integral
-    pure_and_blended_element_ids!(element_ids_dg, element_ids_dgfv, alpha, dg, cache)
-
-    # Loop over pure DG elements
-    @trixi_timeit timer() "pure DG" @threaded for idx_element in eachindex(element_ids_dg)
-        element = element_ids_dg[idx_element]
-        flux_differencing_kernel!(du, u, element, mesh,
-                                  nonconservative_terms, equations,
-                                  volume_flux_dg, dg, cache)
-    end
-
-    # Loop over blended DG-FV elements
-    @trixi_timeit timer() "blended DG-FV" @threaded for idx_element in eachindex(element_ids_dgfv)
-        element = element_ids_dgfv[idx_element]
+    RealT = eltype(alpha)
+    atol = max(100 * eps(RealT), eps(RealT)^convert(RealT, 0.75f0))
+    @threaded for element in eachelement(dg, cache)
         alpha_element = alpha[element]
-
-        # Calculate DG volume integral contribution
-        flux_differencing_kernel!(du, u, element, mesh,
-                                  nonconservative_terms, equations,
-                                  volume_flux_dg, dg, cache, 1 - alpha_element)
-
-        # Calculate FV volume integral contribution
-        fv_kernel!(du, u, mesh, nonconservative_terms, equations, volume_flux_fv,
-                   dg, cache, element, alpha_element)
+        # Clip blending factor for values close to zero (-> pure DG)
+        dg_only = isapprox(alpha_element, 0, atol = atol)
+
+        if dg_only
+            flux_differencing_kernel!(du, u, element, mesh,
+                                      nonconservative_terms, equations,
+                                      volume_flux_dg, dg, cache)
+        else
+            # Calculate DG volume integral contribution
+            flux_differencing_kernel!(du, u, element, mesh,
+                                      nonconservative_terms, equations,
+                                      volume_flux_dg, dg, cache, 1 - alpha_element)
+
+            # Calculate FV volume integral contribution
+            fv_kernel!(du, u, mesh, nonconservative_terms, equations, volume_flux_fv,
+                       dg, cache, element, alpha_element)
+        end
     end
 
     return nothing