--- a/Notes.md	Thu Jul 15 00:28:09 2021 +0200
+++ b/Notes.md	Mon Jul 19 08:47:33 2021 +0200
@@ -330,3 +330,5 @@
 A different approach would be to include it as a trait for operators so that you can specify what the adjoint for that operator is.
 
 
+## Name of the `VolumeOperator` type for constant stencils
+It seems that the name is too general. The name of the method `volume_operator` makes sense. It should return different types of `TensorMapping` specialized for the grid. A suggetion for a better name is `ConstantStencilVolumeOperator`

--- a/src/SbpOperators/SbpOperators.jl	Thu Jul 15 00:28:09 2021 +0200
+++ b/src/SbpOperators/SbpOperators.jl	Mon Jul 19 08:47:33 2021 +0200
@@ -8,7 +8,7 @@
 include("d2.jl")
 include("readoperator.jl")
 include("volumeops/volume_operator.jl")
-include("volumeops/derivatives/secondderivative.jl")
+include("volumeops/derivatives/second_derivative.jl")
 include("volumeops/laplace/laplace.jl")
 include("volumeops/inner_products/inner_product.jl")
 include("volumeops/inner_products/inverse_inner_product.jl")

--- a/src/SbpOperators/boundaryops/boundary_restriction.jl	Thu Jul 15 00:28:09 2021 +0200
+++ b/src/SbpOperators/boundaryops/boundary_restriction.jl	Mon Jul 19 08:47:33 2021 +0200
@@ -9,7 +9,7 @@
 On a one-dimensional `grid`, `e` is a `BoundaryOperator`. On a multi-dimensional `grid`, `e` is the inflation of
 a `BoundaryOperator`. Also see the documentation of `SbpOperators.boundary_operator(...)` for more details.
 """
-boundary_restriction(grid::EquidistantGrid, closure_stencil::Stencil, boundary::CartesianBoundary) = SbpOperators.boundary_operator(grid, closure_stencil, boundary)
-boundary_restriction(grid::EquidistantGrid{1}, closure_stencil::Stencil, region::Region) = boundary_restriction(grid, closure_stencil, CartesianBoundary{1,typeof(region)}())
+boundary_restriction(grid::EquidistantGrid, closure_stencil, boundary::CartesianBoundary) = SbpOperators.boundary_operator(grid, closure_stencil, boundary)
+boundary_restriction(grid::EquidistantGrid{1}, closure_stencil, region::Region) = boundary_restriction(grid, closure_stencil, CartesianBoundary{1,typeof(region)}())
 
 export boundary_restriction

--- a/src/SbpOperators/boundaryops/normal_derivative.jl	Thu Jul 15 00:28:09 2021 +0200
+++ b/src/SbpOperators/boundaryops/normal_derivative.jl	Mon Jul 19 08:47:33 2021 +0200
@@ -9,10 +9,10 @@
 On a one-dimensional `grid`, `d` is a `BoundaryOperator`. On a multi-dimensional `grid`, `d` is the inflation of
 a `BoundaryOperator`. Also see the documentation of `SbpOperators.boundary_operator(...)` for more details.
 """
-function normal_derivative(grid::EquidistantGrid, closure_stencil::Stencil, boundary::CartesianBoundary)
+function normal_derivative(grid::EquidistantGrid, closure_stencil, boundary::CartesianBoundary)
     direction = dim(boundary)
     h_inv = inverse_spacing(grid)[direction]
     return SbpOperators.boundary_operator(grid, scale(closure_stencil,h_inv), boundary)
 end
-normal_derivative(grid::EquidistantGrid{1}, closure_stencil::Stencil, region::Region) = normal_derivative(grid, closure_stencil, CartesianBoundary{1,typeof(region)}())
+normal_derivative(grid::EquidistantGrid{1}, closure_stencil, region::Region) = normal_derivative(grid, closure_stencil, CartesianBoundary{1,typeof(region)}())
 export normal_derivative

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/SbpOperators/volumeops/derivatives/second_derivative.jl	Mon Jul 19 08:47:33 2021 +0200
@@ -0,0 +1,20 @@
+"""
+    second_derivative(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils, direction)
+    second_derivative(grid::EquidistantGrid{1}, inner_stencil, closure_stencils)
+
+Creates the second-derivative operator `D2` as a `TensorMapping`
+
+`D2` approximates the second-derivative d²/dξ² on `grid` along the coordinate dimension specified by
+`direction`, using the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
+for the points in the closure regions.
+
+On a one-dimensional `grid`, `D2` is a `VolumeOperator`. On a multi-dimensional `grid`, `D2` is the outer product of the
+one-dimensional operator with the `IdentityMapping`s in orthogonal coordinate dirrections.
+Also see the documentation of `SbpOperators.volume_operator(...)` for more details.
+"""
+function second_derivative(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils, direction) where Dim
+    h_inv = inverse_spacing(grid)[direction]
+    return SbpOperators.volume_operator(grid, scale(inner_stencil,h_inv^2), scale.(closure_stencils,h_inv^2), even, direction)
+end
+second_derivative(grid::EquidistantGrid{1}, inner_stencil, closure_stencils) = second_derivative(grid,inner_stencil,closure_stencils,1)
+export second_derivative

--- a/src/SbpOperators/volumeops/derivatives/secondderivative.jl	Thu Jul 15 00:28:09 2021 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,20 +0,0 @@
-"""
-    second_derivative(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils, direction)
-    second_derivative(grid::EquidistantGrid{1}, inner_stencil, closure_stencils)
-
-Creates the second-derivative operator `D2` as a `TensorMapping`
-
-`D2` approximates the second-derivative d²/dξ² on `grid` along the coordinate dimension specified by
-`direction`, using the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
-for the points in the closure regions.
-
-On a one-dimensional `grid`, `D2` is a `VolumeOperator`. On a multi-dimensional `grid`, `D2` is the outer product of the
-one-dimensional operator with the `IdentityMapping`s in orthogonal coordinate dirrections.
-Also see the documentation of `SbpOperators.volume_operator(...)` for more details.
-"""
-function second_derivative(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils, direction) where Dim
-    h_inv = inverse_spacing(grid)[direction]
-    return SbpOperators.volume_operator(grid, scale(inner_stencil,h_inv^2), scale.(closure_stencils,h_inv^2), even, direction)
-end
-second_derivative(grid::EquidistantGrid{1}, inner_stencil, closure_stencils) = second_derivative(grid,inner_stencil,closure_stencils,1)
-export second_derivative

--- a/src/SbpOperators/volumeops/volume_operator.jl	Thu Jul 15 00:28:09 2021 +0200
+++ b/src/SbpOperators/volumeops/volume_operator.jl	Mon Jul 19 08:47:33 2021 +0200
@@ -1,14 +1,15 @@
 """
-    volume_operator(grid,inner_stencil,closure_stencils,parity,direction)
+    volume_operator(grid, inner_stencil, closure_stencils, parity, direction)
+
 Creates a volume operator on a `Dim`-dimensional grid acting along the
-specified coordinate `direction`. The action of the operator is determined by the
-stencils `inner_stencil` and `closure_stencils`.
-When `Dim=1`, the corresponding `VolumeOperator` tensor mapping is returned.
-When `Dim>1`, the `VolumeOperator` `op` is inflated by the outer product
-of `IdentityMappings` in orthogonal coordinate directions, e.g for `Dim=3`,
-the boundary restriction operator in the y-direction direction is `Ix⊗op⊗Iz`.
+specified coordinate `direction`. The action of the operator is determined by
+the stencils `inner_stencil` and `closure_stencils`. When `Dim=1`, the
+corresponding `VolumeOperator` tensor mapping is returned. When `Dim>1`, the
+returned operator is the appropriate outer product of a one-dimensional
+operators and `IdentityMapping`s, e.g for `Dim=3` the volume operator in the
+y-direction is `I⊗op⊗I`.
 """
-function volume_operator(grid::EquidistantGrid{Dim,T}, inner_stencil::Stencil{T}, closure_stencils::NTuple{M,Stencil{T}}, parity, direction) where {Dim,T,M}
+function volume_operator(grid::EquidistantGrid{Dim,T}, inner_stencil, closure_stencils, parity, direction) where {Dim,T}
     #TODO: Check that direction <= Dim?
 
     # Create 1D volume operator in along coordinate direction
@@ -34,7 +35,7 @@
 end
 
 function VolumeOperator(grid::EquidistantGrid{1}, inner_stencil, closure_stencils, parity)
-    return VolumeOperator(inner_stencil, closure_stencils, size(grid), parity)
+    return VolumeOperator(inner_stencil, Tuple(closure_stencils), size(grid), parity)
 end
 
 closure_size(::VolumeOperator{T,N,M}) where {T,N,M} = M

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/SbpOperators/volumeops/derivatives/second_derivative_test.jl	Mon Jul 19 08:47:33 2021 +0200
@@ -0,0 +1,108 @@
+using Test
+
+using Sbplib.SbpOperators
+using Sbplib.Grids
+using Sbplib.LazyTensors
+
+import Sbplib.SbpOperators.VolumeOperator
+
+@testset "SecondDerivative" begin
+    op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
+    Lx = 3.5
+    Ly = 3.
+    g_1D = EquidistantGrid(121, 0.0, Lx)
+    g_2D = EquidistantGrid((121,123), (0.0, 0.0), (Lx, Ly))
+
+    @testset "Constructors" begin
+        @testset "1D" begin
+            Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
+            @test Dₓₓ == second_derivative(g_1D,op.innerStencil,op.closureStencils,1)
+            @test Dₓₓ isa VolumeOperator
+        end
+        @testset "2D" begin
+            Dₓₓ = second_derivative(g_2D,op.innerStencil,op.closureStencils,1)
+            D2 = second_derivative(g_1D,op.innerStencil,op.closureStencils)
+            I = IdentityMapping{Float64}(size(g_2D)[2])
+            @test Dₓₓ == D2⊗I
+            @test Dₓₓ isa TensorMapping{T,2,2} where T
+        end
+    end
+
+    # Exact differentiation is measured point-wise. In other cases
+    # the error is measured in the l2-norm.
+    @testset "Accuracy" begin
+        @testset "1D" begin
+            l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2));
+            monomials = ()
+            maxOrder = 4;
+            for i = 0:maxOrder-1
+                f_i(x) = 1/factorial(i)*x^i
+                monomials = (monomials...,evalOn(g_1D,f_i))
+            end
+            v = evalOn(g_1D,x -> sin(x))
+            vₓₓ = evalOn(g_1D,x -> -sin(x))
+
+            # 2nd order interior stencil, 1nd order boundary stencil,
+            # implies that L*v should be exact for monomials up to order 2.
+            @testset "2nd order" begin
+                op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
+                Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
+                @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
+                @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
+                @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
+                @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2
+            end
+
+            # 4th order interior stencil, 2nd order boundary stencil,
+            # implies that L*v should be exact for monomials up to order 3.
+            @testset "4th order" begin
+                op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
+                Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
+                # NOTE: high tolerances for checking the "exact" differentiation
+                # due to accumulation of round-off errors/cancellation errors?
+                @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
+                @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
+                @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
+                @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10
+                @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2
+            end
+        end
+
+        @testset "2D" begin
+            l2(v) = sqrt(prod(spacing(g_2D))*sum(v.^2));
+            binomials = ()
+            maxOrder = 4;
+            for i = 0:maxOrder-1
+                f_i(x,y) = 1/factorial(i)*y^i + x^i
+                binomials = (binomials...,evalOn(g_2D,f_i))
+            end
+            v = evalOn(g_2D, (x,y) -> sin(x)+cos(y))
+            v_yy = evalOn(g_2D,(x,y) -> -cos(y))
+
+            # 2nd order interior stencil, 1st order boundary stencil,
+            # implies that L*v should be exact for binomials up to order 2.
+            @testset "2nd order" begin
+                op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
+                Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2)
+                @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
+                @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
+                @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
+                @test Dyy*v ≈ v_yy rtol = 5e-2 norm = l2
+            end
+
+            # 4th order interior stencil, 2nd order boundary stencil,
+            # implies that L*v should be exact for binomials up to order 3.
+            @testset "4th order" begin
+                op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
+                Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2)
+                # NOTE: high tolerances for checking the "exact" differentiation
+                # due to accumulation of round-off errors/cancellation errors?
+                @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
+                @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
+                @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
+                @test Dyy*binomials[4] ≈ evalOn(g_2D,(x,y)->y) atol = 5e-9
+                @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2
+            end
+        end
+    end
+end

--- a/test/SbpOperators/volumeops/derivatives/secondderivative_test.jl	Thu Jul 15 00:28:09 2021 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,108 +0,0 @@
-using Test
-
-using Sbplib.SbpOperators
-using Sbplib.Grids
-using Sbplib.LazyTensors
-
-import Sbplib.SbpOperators.VolumeOperator
-
-@testset "SecondDerivative" begin
-    op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
-    Lx = 3.5
-    Ly = 3.
-    g_1D = EquidistantGrid(121, 0.0, Lx)
-    g_2D = EquidistantGrid((121,123), (0.0, 0.0), (Lx, Ly))
-
-    @testset "Constructors" begin
-        @testset "1D" begin
-            Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
-            @test Dₓₓ == second_derivative(g_1D,op.innerStencil,op.closureStencils,1)
-            @test Dₓₓ isa VolumeOperator
-        end
-        @testset "2D" begin
-            Dₓₓ = second_derivative(g_2D,op.innerStencil,op.closureStencils,1)
-            D2 = second_derivative(g_1D,op.innerStencil,op.closureStencils)
-            I = IdentityMapping{Float64}(size(g_2D)[2])
-            @test Dₓₓ == D2⊗I
-            @test Dₓₓ isa TensorMapping{T,2,2} where T
-        end
-    end
-
-    # Exact differentiation is measured point-wise. In other cases
-    # the error is measured in the l2-norm.
-    @testset "Accuracy" begin
-        @testset "1D" begin
-            l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2));
-            monomials = ()
-            maxOrder = 4;
-            for i = 0:maxOrder-1
-                f_i(x) = 1/factorial(i)*x^i
-                monomials = (monomials...,evalOn(g_1D,f_i))
-            end
-            v = evalOn(g_1D,x -> sin(x))
-            vₓₓ = evalOn(g_1D,x -> -sin(x))
-
-            # 2nd order interior stencil, 1nd order boundary stencil,
-            # implies that L*v should be exact for monomials up to order 2.
-            @testset "2nd order" begin
-                op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
-                Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
-                @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
-                @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
-                @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
-                @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2
-            end
-
-            # 4th order interior stencil, 2nd order boundary stencil,
-            # implies that L*v should be exact for monomials up to order 3.
-            @testset "4th order" begin
-                op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
-                Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
-                # NOTE: high tolerances for checking the "exact" differentiation
-                # due to accumulation of round-off errors/cancellation errors?
-                @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
-                @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
-                @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
-                @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10
-                @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2
-            end
-        end
-
-        @testset "2D" begin
-            l2(v) = sqrt(prod(spacing(g_2D))*sum(v.^2));
-            binomials = ()
-            maxOrder = 4;
-            for i = 0:maxOrder-1
-                f_i(x,y) = 1/factorial(i)*y^i + x^i
-                binomials = (binomials...,evalOn(g_2D,f_i))
-            end
-            v = evalOn(g_2D, (x,y) -> sin(x)+cos(y))
-            v_yy = evalOn(g_2D,(x,y) -> -cos(y))
-
-            # 2nd order interior stencil, 1st order boundary stencil,
-            # implies that L*v should be exact for binomials up to order 2.
-            @testset "2nd order" begin
-                op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
-                Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2)
-                @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
-                @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
-                @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
-                @test Dyy*v ≈ v_yy rtol = 5e-2 norm = l2
-            end
-
-            # 4th order interior stencil, 2nd order boundary stencil,
-            # implies that L*v should be exact for binomials up to order 3.
-            @testset "4th order" begin
-                op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
-                Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2)
-                # NOTE: high tolerances for checking the "exact" differentiation
-                # due to accumulation of round-off errors/cancellation errors?
-                @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
-                @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
-                @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
-                @test Dyy*binomials[4] ≈ evalOn(g_2D,(x,y)->y) atol = 5e-9
-                @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2
-            end
-        end
-    end
-end