From c57eec1ce822a06b926819bc918febc8b46cbd30 Mon Sep 17 00:00:00 2001
From: Tristan Montoya <montoya.tristan@gmail.com>
Date: Thu, 3 Oct 2024 21:28:57 +0200
Subject: [PATCH] add more docs

---
 docs/src/SpatialDiscretizations.md            | 29 ++++++++++-
 .../SpatialDiscretizations.jl                 | 50 +++++++++++++++----
 2 files changed, 68 insertions(+), 11 deletions(-)

diff --git a/docs/src/SpatialDiscretizations.md b/docs/src/SpatialDiscretizations.md
index 856f73b7..60c2fa57 100644
--- a/docs/src/SpatialDiscretizations.md
+++ b/docs/src/SpatialDiscretizations.md
@@ -17,4 +17,31 @@ In order to define the different geometric reference elements, existing subtypes
 ```
 These element types are used in the constructor for StableSpectralElements.jl's `ReferenceApproximation` type, along with a subtype of `AbstractApproximationType` specifying the nature of the local approximation (and, optionally, the associated volume and facet quadrature rules).
 
-All the information used to define the spatial discretization on the physical domain $\Omega$ is contained within a `SpatialDiscretization` structure, which is constructed using a `ReferenceApproximation` and a `MeshData` from StartUpDG.jl, which are stored as the fields `reference_approximation` and `mesh`. When the constructor for a `SpatialDiscretization` is called, the grid metrics are computed and stored in a `GeometricFactors` structure, with the corresponding field being `geometric_factors`. 
\ No newline at end of file
+All the information used to define the spatial discretization on the physical domain $\Omega$ is contained within a `SpatialDiscretization` structure, which is constructed using a `ReferenceApproximation` and a `MeshData` from StartUpDG.jl, which are stored as the fields `reference_approximation` and `mesh`. When the constructor for a `SpatialDiscretization` is called, the grid metrics are computed and stored in a `GeometricFactors` structure, with the corresponding field being `geometric_factors`. 
+
+## Approximation types 
+Listed below are approximation types supported by StableSpectralElements.jl.
+
+### Tensor-product operators 
+The following subtypes of `AbstractTensorProduct <: AbstractApproximationType` employ tensor-product operators.
+
+```@meta
+CurrentModule = SpatialDiscretizations
+```
+```@docs
+    NodalTensor
+    ModalTensor
+```
+
+### Multidimensional operators 
+The following subtypes of `AbstractMultidimensional <: AbstractApproximationType` employ multidimensional operators. 
+
+```@meta
+CurrentModule = SpatialDiscretizations
+```
+```@docs
+    NodalMulti
+    ModalMulti
+    NodalMultiDiagE
+    ModalMultiDiagE
+```
\ No newline at end of file
diff --git a/src/SpatialDiscretizations/SpatialDiscretizations.jl b/src/SpatialDiscretizations/SpatialDiscretizations.jl
index 13cf603c..97e04557 100644
--- a/src/SpatialDiscretizations/SpatialDiscretizations.jl
+++ b/src/SpatialDiscretizations/SpatialDiscretizations.jl
@@ -68,37 +68,67 @@ export AbstractApproximationType,
 abstract type AbstractApproximationType end
 abstract type AbstractTensorProduct <: AbstractApproximationType end
 abstract type AbstractMultidimensional <: AbstractApproximationType end
+@doc raw"""
+    NodalTensor(p::Int)
 
-"""Nodal approximation using tensor-product operators"""
+Approximation type for a nodal formulation based on tensor-product volume and facet 
+quadrature rules.
+"""
 struct NodalTensor <: AbstractTensorProduct
     p::Int
 end
 
-"""Modal approximation using tensor-product operators"""
+@doc raw"""
+    ModalTensor(p::Int)
+
+Approximation type for a modal formulation based on tensor-product volume and facet 
+quadrature rules.
+"""
 struct ModalTensor <: AbstractTensorProduct
     p::Int
 end
 
-"""Modal approximation using multidimensional operators"""
-struct ModalMulti <: AbstractMultidimensional
-    p::Int
-end
+@doc raw"""
+    NodalMulti(p::Int)
 
-"""Nodal approximation using multidimensional operators"""
+Approximation type for a nodal formulation based on multidimensional volume and facet 
+quadrature rules.
+"""
 struct NodalMulti <: AbstractMultidimensional
     p::Int
 end
 
-"""Modal approximation using diagonal-E SBP operators"""
-struct ModalMultiDiagE <: AbstractMultidimensional
+@doc raw"""
+    ModalMulti(p::Int)
+
+Approximation type for a modal formulation based on a multidimensional volume and facet 
+quadrature rules.
+"""
+struct ModalMulti <: AbstractMultidimensional
     p::Int
 end
 
-"""Nodal approximation using diagonal-E SBP operators"""
+@doc raw"""
+    NodalMultiDiagE(p::Int)
+
+Approximation type for a nodal formulation based on a multidimensional volume quadrature
+rule including nodes collocated with those used for facet integration.
+"""
 struct NodalMultiDiagE <: AbstractMultidimensional
     p::Int
 end
 
+@doc raw"""
+    ModalMultiDiagE(p::Int)
+
+Approximation type for a modal formulation based on a multidimensional volume quadrature
+rule including nodes collocated with those used for facet integration.
+"""
+struct ModalMultiDiagE <: AbstractMultidimensional
+    p::Int
+end
+
+
 """Collapsed coordinate mapping χ: [-1,1]ᵈ → Ωᵣ"""
 abstract type AbstractReferenceMapping end
 struct NoMapping <: AbstractReferenceMapping end