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The promise of hybridizable DG methods {#Sec:promiseHDG}
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In the Introduction some properties and advantages of DG and HDG methods were briefly mentioned, which we here explain in more detail. The classic DG method is seldomly employed for solving stationary problems, because it duplicates degrees of freedom (DOFs) on every internal edge. Thus the number of globally coupled DOFs is much greater than the number of DOFs required by conforming finite element methods for the same accuracy. Consequently, DG methods are expensive in terms of both CPU time and memory consumption. Hybridization of DG methods [@CGL2009] is devoted to addressing this issue while at the same time keeping all the advantages of DG methods. HDG methods introduce additional hybrid variables on the edges of the elements. Then we define the numerical traces arising from partial integration in the DG formulations through the hybrid variables. We can thus define the local (element-wise) solutions by hybrid variables. Conservativity conditions are imposed on numerical traces to ensure the continuity of the tangential component of the electric field and the normal component of the current density and to make the problem solvable. As a result, HDG methods produce a linear system in terms 