🎨 Update theme to article-theme

.github/workflows/deploy.yml

@@ -1,3 +1,5 @@
+# This file was created automatically with `myst init --gh-pages` 🪄 💚
+
 name: MyST GitHub Pages Deploy
 on:
   push:

myst.yml

@@ -17,17 +17,30 @@ project:
       orcid: 0000-0002-7859-8394
       corresponding: true
       email: [email protected]
-      affiliations:
-        - University of British Columbia
+      twitter: rowancockett
+      github: rowanc1
+      affiliation: ubc
+      roles: writing
+      url: https://row1.ca
     - name: Lindsey Heagy
       orcid: 0000-0002-1551-5926
-      affiliations:
-        - University of British Columbia
+      affiliation: ubc
     - name: Douglas Oldenburg
       orcid: 0000-0002-4327-2124
-      affiliations:
-        - University of British Columbia
-  thebe:
+      affiliation: ubc
+  affiliations:
+    - id: ubc
+      institution: University of British Columbia
+      ror: https://ror.org/03rmrcq20
+      isni: 0000 0001 2288 9830
+      department: Department of Earth, Ocean and Atmospheric Sciences
+      address: 2020 – 2207 Main Mall
+      city: Vancouver
+      region: British Columbia
+      country: Canada
+      postal_code: V6T 1Z4
+      phone: 1 (604) 822-2449
+  jupyter:
     binder:
       url: https://xhrtcvh6l53u.curvenote.dev/services/binder/
       repo: curvenote/tle-finitevolume
@@ -50,8 +63,10 @@ project:
     - requirements.txt
   resources:
     - all-together-now.ipynb
+  banner: ./images/banner.png
 site:
   title: 'Pixels and Their Neighbours: Finite Volume'
+  template: article-theme
   actions:
     - title: Download PDF
       url: ./cockett-heagy-oldenburg-2016.pdf

paper.md

@@ -86,7 +86,7 @@ $$\text{v} \mathbf{D}\mathbf{j} = q$$ (eq:div)
 
 ## (2) Scalar equations only, please
 
-Equation [](#eq:div) is a vector equation, so really it is two or three equations involving multiple components of $\vec{j}$. We want to work with a single scalar equation, allow for anisotropic physical properties, and potentially work with non-axis-aligned meshes - how do we do this?! We can use the **weak formulation** where we take the inner product ($\int \vec{a} \cdot \vec{b} dv$) of the equation with a generic face function, $\vec{f}$. This reduces requirements of differentiability on the original equation and also allows us to consider tensor anisotropy or curvilinear meshes .
+Equation [](#eq:div) is a vector equation, so really it is two or three equations involving multiple components of $\vec{j}$. We want to work with a single scalar equation, allow for anisotropic physical properties, and potentially work with non-axis-aligned meshes - how do we do this?! We can use the **weak formulation** where we take the inner product ($\int \vec{a} \cdot \vec{b} dv$) of the equation with a generic face function, $\vec{f}$. This reduces requirements of differentiability on the original equation and also allows us to consider tensor anisotropy or curvilinear meshes.
 
 In [](#fig-weak-formulation), we visually walk through the discretization of equation (b). On the left hand side, a dot product requires a _single_ cartesian vector, $\mathbf{j_x, j_y}$. However, we have a $j$ defined on each face (2 $j_x$ and 2 $j_y$ in 2D!). There are many different ways to evaluate this inner product: we could approximate the integral using trapezoidal, midpoint or higher order approximations. A simple method is to break the integral into four sections (or 8 in 3D) and apply the midpoint rule for each section using the closest $\mathbf{j}$ components to compose a cartesian vector. A $\mathbf{P}_i$ matrix (size $2 \times 4$) is used to pick out the appropriate faces and compose the corresponding vector (these matrices are shown with colors corresponding to the appropriate face in the figure). On the right hand side, we use a vector identity to integrate by parts. The second term will cancel over the entire mesh (as the normals of adjacent cell faces point in opposite directions) and $\phi$ on mesh boundary faces are zero by the Dirichlet boundary condition. This leaves us with the divergence, which we already know how to do!