--- a/src/SbpOperators/volumeops/derivatives/second_derivative.jl	Fri Jan 21 15:23:08 2022 +0100
+++ b/src/SbpOperators/volumeops/derivatives/second_derivative.jl	Sun Jan 12 21:18:44 2025 +0100
@@ -1,19 +1,37 @@
 """
-    second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction)
+    second_derivative(g::EquidistantGrid, stencil_set, direction)
+
+Creates the second derivative operator `D2` as a `LazyTensor`
+
+`D2` approximates the second-derivative d²/dξ² on `g` along the coordinate
+dimension specified by `direction`.
 
-Creates the second-derivative operator `D2` as a `TensorMapping`
+See also: [`VolumeOperator`](@ref), [`LazyTensors.inflate`](@ref).
+"""
+function second_derivative(g::TensorGrid, stencil_set, direction)
+    D₂ = second_derivative(g.grids[direction], stencil_set)
+    return LazyTensors.inflate(D₂, size(g), direction)
+end
 
-`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.
+"""
+    second_derivative(g::EquidistantGrid, stencil_set::::StencilSet)
 
-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.
+The second derivative operator on an `EquidistantGrid`. 
+Uses the `D2` stencil in `stencil_set`.
+"""
+function second_derivative(g::EquidistantGrid, stencil_set::StencilSet)
+    inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
+    closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
+    return second_derivative(g, inner_stencil, closure_stencils)
+end
+
 """
-function second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction)
-    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)
+    second_derivative(g::EquidistantGrid, inner_stencil::Stencil, closure_stencils)
+
+The second derivative operator on an `EquidistantGrid`, given `inner_stencil` and
+`closure_stencils`.
+"""
+function second_derivative(g::EquidistantGrid, inner_stencil::Stencil, closure_stencils)
+    h⁻¹ = inverse_spacing(g)
+    return VolumeOperator(g, scale(inner_stencil,h⁻¹^2), scale.(closure_stencils,h⁻¹^2), even)
 end
-second_derivative(grid::EquidistantGrid{1}, inner_stencil, closure_stencils) = second_derivative(grid,inner_stencil,closure_stencils,1)
-export second_derivative