--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/SbpOperators/boundary_conditions/sat_test.jl	Tue Jun 04 16:46:14 2024 -0700
@@ -0,0 +1,71 @@
+using Test
+
+using Sbplib.Grids
+using Sbplib.LazyTensors
+using Sbplib.SbpOperators
+
+stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order = 4)
+
+struct MockOp end
+
+function SbpOperators.sat_tensors(op::MockOp, g::Grid, bc::DirichletCondition; a = 1.)
+    e = boundary_restriction(g, stencil_set, boundary(bc))
+    L = a*e
+    sat_op = e'
+    return sat_op, L
+end
+
+function SbpOperators.sat_tensors(op::MockOp, g::Grid, bc::NeumannCondition)
+    e = boundary_restriction(g, stencil_set, boundary(bc))
+    d = normal_derivative(g, stencil_set, boundary(bc))
+    L = d
+    sat_op = e'
+    return sat_op, L
+end
+
+@testset "sat" begin
+    op = MockOp()
+    @testset "1D" begin
+        grid  = equidistant_grid(0., 1., 11)
+        l, r = boundary_identifiers(grid)
+        u = eval_on(grid, x-> 1. + 2x^2)
+        dc = DirichletCondition(1.0, l)
+        g_l = discretize_data(grid, dc)
+        SAT_l = sat(op, grid, dc)
+        @test SAT_l(u, g_l) ≈ zeros((size(grid))) atol = 1e-13
+        
+        nc = NeumannCondition(4.0, r)
+        g_r = discretize_data(grid, nc)
+        SAT_r = sat(op, grid, nc)
+        @test SAT_r(u, g_r) ≈ zeros((size(grid))) atol = 1e-13
+    end
+    @testset "2D" begin
+        grid  = equidistant_grid((0.,0.), (1.,1.), 11, 13)
+        W, E, S, N = boundary_identifiers(grid)
+        u = eval_on(grid, (x,y) -> x+y^2)
+
+        dc_W = DirichletCondition(1.0, W)
+        SAT_W = sat(op, grid, dc_W)
+        g_W = discretize_data(grid, dc_W)
+        r_W = zeros(size(grid))
+        r_W[1,:] .= map(y -> (y^2-1.), range(0., 1., length=13))
+        @test SAT_W(u, g_W) ≈ r_W atol = 1e-13
+
+        dc_E = DirichletCondition(2, E)
+        SAT_E = sat(op, grid, dc_E; a = 2.)
+        g_E = discretize_data(grid, dc_E)
+        r_E = zeros(size(grid))
+        r_E[end,:] .= map(y -> (2*(1. + y^2)-2.), range(0., 1., length=13))
+        @test SAT_E(u, g_E) ≈ r_E atol = 1e-13
+
+        nc_S = NeumannCondition(.0, S)
+        SAT_S = sat(op, grid, nc_S)
+        g_S = discretize_data(grid, nc_S)
+        @test SAT_S(u, g_S) ≈ zeros(size(grid)) atol = 1e-13
+
+        nc_N = NeumannCondition(2.0, N)
+        SAT_N = sat(op, grid, nc_N)
+        g_N = discretize_data(grid, nc_N)
+        @test SAT_N(u, g_N) ≈ zeros(size(grid)) atol = 1e-13
+    end
+end