Check docs build as part of CI

.github/workflows/docs.yml

@@ -0,0 +1,57 @@
+name: Check docs build cleanly
+
+on:
+  # Run on pushes to master
+  push:
+    branches:
+      - master
+  # And all pull requests
+  pull_request:
+
+concurrency:
+  # Cancels jobs running if new commits are pushed
+  group: >
+    ${{ github.workflow }}-
+    ${{ github.event.pull_request.number || github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  build_docs:
+    name: Run doc build
+    # The type of runner that the job will run on
+    runs-on: ubuntu-latest
+    # The docker container to use.
+    container:
+      image: firedrakeproject/firedrake-docdeps:latest
+      options: --user root
+      volumes:
+        - ${{ github.workspace }}:/home/firedrake/output
+    # Steps represent a sequence of tasks that will be executed as
+    # part of the jobs
+    steps:
+      - uses: actions/checkout@v3
+      - name: Install checkedout Gusto
+        run: |
+          . /home/firedrake/firedrake/bin/activate
+          python -m pip install -e .
+      - name: Install Read the Docs theme
+        run: |
+          . /home/firedrake/firedrake/bin/activate
+          python -m pip install sphinx_rtd_theme
+      - name: Check documentation links
+        if: ${{ github.ref == 'refs/heads/master' }}
+        run: |
+          . /home/firedrake/firedrake/bin/activate
+          cd docs
+          make linkcheck
+      - name: Build docs
+        run: |
+          . /home/firedrake/firedrake/bin/activate
+          cd docs
+          make html
+      - name: Upload artifact
+        uses: actions/upload-pages-artifact@v1
+        with:
+          name: github-pages
+          path: /__w/gusto/gusto/docs/build/html
+          retention-days: 1