--- a/src/SbpOperators/volumeops/laplace/laplace.jl	Sun Jan 31 20:59:29 2021 +0100
+++ b/src/SbpOperators/volumeops/laplace/laplace.jl	Sun Jan 31 21:04:02 2021 +0100
@@ -1,5 +1,77 @@
 """
-    Laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils)
+    Laplace{T,Dim,...}()
+    Laplace(grid::EquidistantGrid, fn; order)
+
+Implements the Laplace operator, approximating ∑d²/xᵢ² , i = 1,...,`Dim` as a
+`TensorMapping`. Additionally, `Laplace` stores the quadrature, and boundary
+operators relevant for constructing a SBP finite difference scheme as `TensorMapping`s.
+"""
+struct Laplace{T, Dim, Rb, TMdiffop<:TensorMapping{T,Dim,Dim}, # Differential operator tensor mapping
+                           TMqop<:TensorMapping{T,Dim,Dim}, # Quadrature operator tensor mapping
+                           TMbop<:TensorMapping{T,Rb,Dim}, # Boundary operator tensor mapping
+                           TMbqop<:TensorMapping{T,Rb,Rb}, # Boundary quadrature tensor mapping
+                           BID<:BoundaryIdentifier} <: TensorMapping{T,Dim,Dim}
+    D::TMdiffop # Difference operator
+    H::TMqop # Quadrature (norm) operator
+    H_inv::TMqop # Inverse quadrature (norm) operator
+    e::Dict{BID,TMbop} # Boundary restriction operators
+    d::Dict{BID,TMbop} # Normal derivative operators
+    H_boundary::Dict{BID,TMbqop} # Boundary quadrature operators
+end
+export Laplace
+
+function Laplace(grid::EquidistantGrid, fn; order)
+    # TODO: Removed once we can construct the volume and
+    # boundary operators by op(grid, fn; order,...).
+    # Read stencils
+    op = read_D2_operator(fn; order)
+    D_inner_stecil = op.innerStencil
+    D_closure_stencils = op.closureStencils
+    H_closure_stencils = op.quadratureClosure
+    e_closure_stencil = op.eClosure
+    d_closure_stencil = op.dClosure
+
+    # Volume operators
+    Δ =  laplace(grid, D_inner_stecil, D_closure_stencils)
+    H =  DiagonalQuadrature(grid, H_closure_stencils)
+    H⁻¹ =  InverseDiagonalQuadrature(grid, H_closure_stencils)
+
+    # Pair boundary operators and boundary quadratures with the boundary ids
+    e_pairs = ()
+    d_pairs = ()
+    Hᵧ_pairs = ()
+    dims = collect(1:dimension(grid))
+    for id ∈ boundary_identifiers(grid)
+        # Boundary operators
+        e_pairs = (e_pairs...,Pair(id,BoundaryRestriction(grid,e_closure_stencil,id)))
+        d_pairs = (d_pairs...,Pair(id,NormalDerivative(grid,d_closure_stencil,id)))
+        # Boundary quadratures
+        # Construct these on the lower-dimensional grid in the
+        # coordinite directions orthogonal to dim(id)
+        orth_dims = dims[dims .!= dim(id)]
+        orth_grid = restrict(grid,orth_dims)
+        Hᵧ_pairs = (Hᵧ_pairs...,Pair(id,DiagonalQuadrature(orth_grid,H_closure_stencils)))
+    end
+    return Laplace(Δ, H, H⁻¹, Dict(e_pairs), Dict(d_pairs), Dict(Hᵧ_pairs))
+end
+
+LazyTensors.range_size(L::Laplace) = LazyTensors.range_size(L.D)
+LazyTensors.domain_size(L::Laplace) = LazyTensors.domain_size(L.D)
+LazyTensors.apply(L::Laplace, v::AbstractArray, I...) = LazyTensors.apply(L.D,v,I...)
+
+quadrature(L::Laplace) = L.H
+export quadrature
+inverse_quadrature(L::Laplace) = L.H_inv
+export inverse_quadrature
+boundary_restriction(L::Laplace,bid::BoundaryIdentifier) = L.e[bid]
+export boundary_restriction
+normal_derivative(L::Laplace,bid::BoundaryIdentifier) = L.d[bid]
+export normal_derivative
+boundary_quadrature(L::Laplace,bid::BoundaryIdentifier) = L.H_boundary[bid]
+export boundary_quadrature
+
+"""
+    laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils)
 
 Creates the Laplace operator operator `Δ` as a `TensorMapping`
 
@@ -10,11 +82,11 @@
 On a one-dimensional `grid`, `Δ` is a `SecondDerivative`. On a multi-dimensional `grid`, `Δ` is the sum of
 multi-dimensional `SecondDerivative`s where the sum is carried out lazily.
 """
-function Laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils) where Dim
+function laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils) where Dim
     Δ = SecondDerivative(grid, inner_stencil, closure_stencils, 1)
     for d = 2:Dim
         Δ += SecondDerivative(grid, inner_stencil, closure_stencils, d)
     end
     return Δ
 end
-export Laplace
+export laplace