Mixed finite elements are among the methods that many people use to discretize elliptic and parabolic second order initial and boundary value problems. The mixed finite element method is particularly useful when local (with respect to the finite elements) mass conservation is essential for the application. For this reason such discretization techniques are widely used to solve numerically various flow problems and other problems in continuous mechanics.

I am interested in the theory and implementation issues of the mixed finite element method. Recently, I have been working on developing efficient iterative techniques for solving discrete problems arising from mixed discretizations of Stokes problems and second order elliptic and parabolic equations. One of my recent papers, Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems. Technical Report ISC-94-09-MATH. (to appear in SIAM J. Num. Anal.), provides a new analysis for the inexact Uzawa algorithm applied to the solution of linear saddle point systems that typically arrise when such problems are solved numerically.