New hybridization techniques

In this paper we present an overview of some new hybridization techniques for linear secondorder elliptic problems. We begin by introducing the hybridization technique through a simple one dimensional example. We then introduce a new point of view with which previously unsuspected applications of hybridization have become possible. Presentation of these applications is the main objective of this review. One such application is in comparing and establishing connections between mixed methods. Next we show how hybridization makes possible the construction of high order variable degree mixed methods. We develop a new error analysis for mixed methods making essential use of hybridization resulting in new error estimates for our new as well as old methods. Finally, we show that via hybridization one can solve the long standing research problem of computing numerical approximations to Stokes flow that are exactly divergence free. We show this for a discontinuous Galerkin method and then for a classical mixed method. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)