# New applications of hybridization for the Dirichlet problem

## Prof. Jay Gopalakrishnan

**July 21, 2004, 11:45 a.m. T 1010**

In this talk, we will discuss a new characterization of the numerical solution given by hybridized mixed methods for the Dirichlet problem. This result has several applications. It allows us to obtain simple and explicit formulae for the entries of the matrix equation for the Lagrange multiplier unknowns arising from hybridization. It leads to the development of efficient preconditioners. It also helps us uncover a previously unsuspected relationship between two popular independently developed hybridizable mixed methods, namely the Raviart-Thomas and the Brezzi-Douglas-Marini methods. Hybridization allows us to construct variable degree versions of these methods with ease. We will show that hybridization has theoretical uses as well by developing a technique of error analysis by which the error estimates for all variables can be obtained as corollaries of error estimates for the Lagrange multipliers. While some of the error estimates obtained this way are known, others are new.