• As the name implies, DG methods employ discontinuous finite element basis functions.
• The finite element solution is piecewise-discontinuous across element boundaries, and continuous within each element.
• DG formulations for elliptic problems are unstable unless special "penalty" terms are employed (see, e.g. "interior penalty DG" method).
• You can use DG in MOOSE by specifying a discontinuous family of basis functions (e.g. MONOMIALS) and adding one or more DGKernels
• DGKernels can execute alongside regular Kernels.
• DGKernels are responsible for computing residual and Jacobian contributions due to the "jump" terms along inter-element edges/faces.