--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/SbpOperators/boundary_conditions/sat.jl	Tue Jun 25 15:32:19 2024 +0200
@@ -0,0 +1,25 @@
+"""
+    sat_tensors(op, grid, bc::BoundaryCondition; kwargs...)
+
+The penalty tensor and boundary operator used to construct a
+simultaneous-approximation-term for imposing `bc` related to `op`.
+
+For `penalty_tensor, L  = sat_tensors(...)` then `SAT(u,g) =
+penalty_tensor*(L*u - g)`  where `g` is the boundary data.
+"""
+function sat_tensors end
+
+
+"""
+    sat(op, grid, bc::BoundaryCondition; kwargs...)
+
+Simultaneous-Approximation-Term for a general `bc` to `op`. Returns a function
+`SAT(u,g)` weakly imposing `bc` when added to `op*u`.
+
+Internally `sat_tensors(op, grid, bc; ...)` is called to construct the
+necessary parts for the SAT.
+"""
+function sat(op, grid, bc::BoundaryCondition; kwargs...)
+    penalty_tensor, L = sat_tensors(op, grid, bc; kwargs...)
+    return SAT(u, g) = penalty_tensor*(L*u - g)
+end