--- a/test/SbpOperators/volumeops/derivatives/first_derivative_test.jl	Tue Mar 15 06:53:06 2022 +0100
+++ b/test/SbpOperators/volumeops/derivatives/first_derivative_test.jl	Tue Mar 15 07:29:41 2022 +0100
@@ -3,3 +3,50 @@
 using Sbplib.SbpOperators
 using Sbplib.Grids
 
+using Sbplib.SbpOperators: closure_size
+
+"""
+    monomial(x,k)
+
+Evaluates ``x^k/k!` with the convetion that it is ``0`` for all ``k<0``.
+Has the property that ``d/dx monomial(x,k) = monomial(x,k-1)``
+"""
+function monomial(x,k)
+    if k < 0
+        return zero(x)
+    end
+    x^k/factorial(k)
+end
+
+@testset "first_derivative" begin
+    @testset "accuracy" begin
+        N = 20
+        g = EquidistantGrid(N, 0//1,2//1)
+        @testset for order ∈ [2,4]
+            stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order)
+            D₁ = first_derivative(g, stencil_set, 1)
+
+            @testset "boundary accuracy $k" for k ∈ 0:order÷2
+                v = evalOn(g, x->monomial(x,k))
+
+                @testset for i ∈ 1:closure_size(D₁)
+                    x, = points(g)[i]
+                    @test (D₁*v)[i] == monomial(x,k-1)
+                end
+
+                @testset for i ∈ (N-closure_size(D₁)+1):N
+                    x, = points(g)[i]
+                    @test (D₁*v)[i] == monomial(x,k-1)
+                end
+            end
+
+            @testset "interior accuracy $k" for k ∈ 0:order
+                v = evalOn(g, x->monomial(x,k))
+
+                x, = points(g)[10]
+                @test (D₁*v)[10] == monomial(x,k-1)
+            end
+        end
+    end
+end
+