--- a/src/SbpOperators/volumeops/quadratures/quadrature.jl	Sun Jan 31 20:57:58 2021 +0100
+++ b/src/SbpOperators/volumeops/quadratures/quadrature.jl	Sat Feb 06 12:03:46 2021 +0100
@@ -1,36 +1,69 @@
 """
-    Quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils)
+    quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils)
+    quadrature(grid::EquidistantGrid, closure_stencils)
 
 Creates the quadrature operator `H` as a `TensorMapping`
 
-The quadrature approximates the integral operator on the grid using
+`H` approximiates the integral operator on `grid` the using the stencil
 `inner_stencil` in the interior and a set of stencils `closure_stencils`
-for the points in the closure regions.
+for the points in the closure regions. If `inner_stencil` is omitted a central
+interior stencil with weight 1 is used.
 
 On a one-dimensional `grid`, `H` is a `VolumeOperator`. On a multi-dimensional
 `grid`, `H` is the outer product of the 1-dimensional quadrature operators in
 each coordinate direction. Also see the documentation of
 `SbpOperators.volume_operator(...)` for more details.
 """
-function Quadrature(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils) where Dim
+function quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils) where Dim
     h = spacing(grid)
     H = SbpOperators.volume_operator(grid, scale(inner_stencil,h[1]), scale.(closure_stencils,h[1]), even, 1)
-    for i ∈ 2:Dim
+    for i ∈ 2:dimension(grid)
         Hᵢ = SbpOperators.volume_operator(grid, scale(inner_stencil,h[i]), scale.(closure_stencils,h[i]), even, i)
         H = H∘Hᵢ
     end
     return H
 end
-export Quadrature
+export quadrature
+
+function quadrature(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T}}) where {M,T}
+    inner_stencil = Stencil(Tuple{T}(1),center=1)
+    return quadrature(grid, inner_stencil, closure_stencils)
+end
 
 """
-    DiagonalQuadrature(grid::EquidistantGrid, closure_stencils)
+    boundary_quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils, id::CartesianBoundary)
+    boundary_quadrature(grid::EquidistantGrid{1}, inner_stencil, closure_stencils, id)
+    boundary_quadrature(grid::EquidistantGrid, closure_stencils, id)
 
-Creates the quadrature operator with the inner stencil 1/h and 1-element sized
-closure stencils (i.e the operator is diagonal)
+Creates the lower-dimensional quadrature operator associated with the boundary
+of `grid` specified by `id`. The quadrature operator is defined on the grid
+spanned by the dimensions orthogonal to the boundary coordinate direction.
+If the dimension of `grid` is 1, then the boundary quadrature is the 0-dimensional
+`IdentityMapping`. If `inner_stencil` is omitted a central interior stencil with
+weight 1 is used.
 """
-function DiagonalQuadrature(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T,1}}) where {M,T}
+function boundary_quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils, id::CartesianBoundary)
+    return quadrature(orthogonal_grid(grid,dim(id)),inner_stencil,closure_stencils)
+end
+export boundary_quadrature
+
+function boundary_quadrature(grid::EquidistantGrid{1}, inner_stencil::Stencil{T}, closure_stencils::NTuple{M,Stencil{T}}, id::CartesianBoundary{1}) where {M,T}
+    return IdentityMapping{T}()
+end
+
+function boundary_quadrature(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T}}, id::CartesianBoundary) where {M,T}
     inner_stencil = Stencil(Tuple{T}(1),center=1)
-    return Quadrature(grid, inner_stencil, closure_stencils)
+    return boundary_quadrature(grid,inner_stencil,closure_stencils,id)
 end
-export DiagonalQuadrature
+
+"""
+    orthogonal_grid(grid,dim)
+
+Creates the lower-dimensional restriciton of `grid` spanned by the dimensions
+orthogonal to `dim`.
+"""
+function orthogonal_grid(grid,dim)
+    dims = collect(1:dimension(grid))
+    orth_dims = dims[dims .!= dim]
+    return restrict(grid,orth_dims)
+end