--- a/src/SbpOperators/volumeops/derivatives/second_derivative_variable.jl	Fri Jan 21 13:20:33 2022 +0100
+++ b/src/SbpOperators/volumeops/derivatives/second_derivative_variable.jl	Fri Jan 28 10:37:57 2022 +0100
@@ -47,18 +47,20 @@
 LazyTensors.domain_size(op::SecondDerivativeVariable) = op.size
 
 function LazyTensors.apply(op::SecondDerivativeVariable{T}, v::AbstractVector{T}, i::Index{Lower}) where T
-    return @inbounds apply_stencil(op.closure_stencils[Int(i)], v, Int(i))
+    return @inbounds apply_stencil(op.closure_stencils[Int(i)], op.coefficient, v, Int(i))
 end
 
 function LazyTensors.apply(op::SecondDerivativeVariable{T}, v::AbstractVector{T}, i::Index{Interior}) where T
-    return apply_stencil(op.inner_stencil, v, Int(i))
+    return apply_stencil(op.inner_stencil, op.coefficient, v, Int(i))
 end
 
 function LazyTensors.apply(op::SecondDerivativeVariable{T}, v::AbstractVector{T}, i::Index{Upper}) where T
-    return @inbounds Int(op.parity)*apply_stencil_backwards(op.closure_stencils[op.size[1]-Int(i)+1], v, Int(i))
+    return @inbounds apply_stencil_backwards(op.closure_stencils[op.size[1]-Int(i)+1], op.coefficient, v, Int(i))
 end
 
 function LazyTensors.apply(op::SecondDerivativeVariable{T}, v::AbstractVector{T}, i) where T
     r = getregion(i, closure_size(op), op.size[1])
     return LazyTensors.apply(op, v, Index(i, r))
 end
+
+# TODO: Rename SecondDerivativeVariable -> VariableSecondDerivative

--- a/test/SbpOperators/volumeops/derivatives/second_derivative_variable_test.jl	Fri Jan 21 13:20:33 2022 +0100
+++ b/test/SbpOperators/volumeops/derivatives/second_derivative_variable_test.jl	Fri Jan 28 10:37:57 2022 +0100
@@ -11,10 +11,9 @@
     g = EquidistantGrid(11, 0., 1.)
     c = [  1,  3,  6, 10, 15, 21, 28, 36, 45, 55, 66]
 
-    interior_stencil = CenteredNestedStencil((-1/2,  -1/2, 0.),( 1/2,     1.,  1/2),(   0.,  -1/2, -1/2))
+    interior_stencil = CenteredNestedStencil((1/2, 1/2, 0.),(-1/2, -1., -1/2),( 0., 1/2, 1/2))
     closure_stencils = [
-        NestedStencil(( 1/2,  1/2, 0.),(-1/2, -1/2,  0.), center = 1),
-        NestedStencil((-1/2, -1/2, 0.),( 1/2,   1., 1/2), center = 2),
+        NestedStencil(( 2.,  -1., 0.),(-3., 1.,  0.), (1., 0., 0.), center = 1),
     ]
 
     @testset "Constructors" begin
@@ -24,13 +23,26 @@
 
     @testset "sizes" begin
         D₂ᶜ = SecondDerivativeVariable(g, c, interior_stencil, closure_stencils)
-        @test closure_size(D₂ᶜ) == 2
+        @test closure_size(D₂ᶜ) == 1
         @test range_size(D₂ᶜ) == (11,)
         @test domain_size(D₂ᶜ) == (11,)
     end
 
     @testset "application" begin
-        # @test D₂(c)*v =
+
+        function apply_to_functions(;v,c)
+            g = EquidistantGrid(11, 0., 10.) # h = 1
+            c̄ = evalOn(g,c)
+            v̄ = evalOn(g,v)
+
+            D₂ᶜ = SecondDerivativeVariable(g, c̄, interior_stencil, closure_stencils)
+            return D₂ᶜ*v̄
+        end
+
+        @test apply_to_functions(v=x->1., c=x->-1.) == zeros(11)
+        @test apply_to_functions(v=x->1., c=x->-x) == zeros(11)
+        @test apply_to_functions(v=x->x, c=x-> 1.) == zeros(11)
+        @test apply_to_functions(v=x->x, c=x->-x) == -ones(11)
     end
 end