The Discontinuous Galerkin (DG) method
was initially introduced by Reed and Hill in 1973 as a
technique to solve neutron transport problems. Lesaint
presented the first numerical analysis of the method for
a linear advection equation. However, the technique has
only recently become popular as a method for solving fluid
dynamics or electromagnetic problems.

The Discontinuous Galerkin method is
somewhere between a finite element and a finite volume
method and has many good features of both. It provides
a practical framework for the development of high-order
accurate methods using unstructured grids. The method
is well suited for large-scale time-dependent computations
in which high accuracy is required. An important distinction
between the DG method and the usual finite-element method
is that in the DG method the resulting equations are local
to the generating element. The solution within each element
is not reconstructed by looking to neighboring elements.
Its compact formulation can be applied near boundaries
without specail treatment, which greatly increases the
robustness and accuracy of any boundary condition implementation.