--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/BoundaryConditions/sat.jl	Tue Oct 11 18:15:47 2022 +0200
@@ -0,0 +1,62 @@
+"""
+    sat_tensors(op, grid, bc::BoundaryCondition{T}, params...)
+
+Returns the `LazyTensor`s used to construct a SAT for the SBP operator `op` on 
+`grid` associated with the boundary condition `bc`.
+"""
+function sat_tensors end
+
+"""
+    sat(op, grid, bc::BoundaryCondition{ConstantBoundaryData{T}}, params...)
+
+Simultaneous-Approximation-Term for constant boundary data. f = sat(op, grid, bc) returns
+an anonymous function, such that f(u) is a `LazyTensorApplication` weakly imposing the BC.
+"""
+function sat(op, grid, bc::BoundaryCondition{ConstantBoundaryData{T}}, params...) where T
+    closure, penalty = sat_tensors(op, grid, bc, params...)
+    b_sz = size(boundary_grid(grid, bc.id))
+    g = fill(data(bc), b_sz)
+    if iszero(g)
+        return u -> closure(u)
+    else
+        return u -> closure(u) + penalty(g)
+    end
+end
+
+"""
+    sat(op, grid, bc::BoundaryCondition{SpaceDependentBoundaryData{T}}, params...)
+
+Simultaneous-Approximation-Term for space-dependent boundary data. f = sat(op, grid, bc) returns
+an anonymous function, such that f(u) is a `LazyTensorApplication` weakly imposing the BC.
+"""
+function sat(op, grid, bc::BoundaryCondition{SpaceDependentBoundaryData{T}}, params...) where T
+    closure, penalty = sat_tensors(op, grid, bc, params...)
+    g = data(bc)
+    return u -> closure(u) + penalty(g)
+end
+
+"""
+    sat(op, grid, bc::BoundaryCondition{SpaceDependentBoundaryData{T}}, params...)
+
+Simultaneous-Approximation-Term for time-dependent boundary data. f = sat(op, grid, bc) returns
+an anonymous function, such that f(u,t) is a `LazyTensorApplication` weakly imposing the BC at time t.
+"""
+function sat(op, grid, bc::BoundaryCondition{TimeDependentBoundaryData{T}}, params...) where T
+    closure, penalty = sat_tensors(op, grid, bc, params...)
+    b_sz = size(boundary_grid(grid, bc.id))
+    b_vec = ones(eltype(grid), b_sz)
+    g = data(bc)
+    return (u,t) -> closure(u) + g(t)*penalty(b_vec)
+end
+
+"""
+    sat(op, grid, bc::BoundaryCondition{SpaceDependentBoundaryData{T}}, params...)
+
+Simultaneous-Approximation-Term for space-time-dependent boundary data. f = sat(op, grid, bc) returns
+an anonymous function, such that f(u,t) is a `LazyTensorApplication` weakly imposing the BC at time t.
+"""
+function sat(op, grid, bc::BoundaryCondition{SpaceTimeDependentBoundaryData{T}}, params...) where T
+    closure, penalty = sat_tensors(op, grid, bc, params...)
+    g = data(bc)
+    return (u,t) -> closure(u) + penalty(g(t))
+end
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