HDG methods for second-order elliptic problems
In this talk, we discuss a new class of discontinuous Galerkin methods called hybridizable. Their distinctive feature is that the only globally-coupled degrees of freedom are those of the numerical trace of the scalar variable. This renders them efficiently implementable. Moreover, they are more precise than all other discontinuous Galerkin methods as thet share with mixed methods their superconvergence properties in the scalar variable and their optimal order of convergence for the vector variable. We are going to show how to devise these methods and comment on their implementation and convergence properties.