mappings. The partial differential equations are first written as a first
order system, and each field is then discretized via a DG method. At this
point, the single-valued "trace" values on the skeleton of the
-mesh, i.e. element faces, are taken to be independent unknown quantities.
+mesh, i.e., element faces, are taken to be independent unknown quantities.
This yields unknowns in the discrete formulation that fall into two categories:
- Face unknowns that only couple with the cell unknowns from both sides of the face;
- Cell unknowns that only couple with the cell and face unknowns
solution that converges at the rate $\mathcal{O}(h^{p+2})$.
+<h4> Alternative approaches </h4>
+
+The hybridizable discontinuous Galerkin method is only one way in
+which the problems of the discontinuous Galerkin method can be
+addressed. Another idea is what is called the "weak Galerkin"
+method. It is explored in step-61.
+
<h3> HDG applied to the convection-diffusion problem </h3>