Saddle Point Problems

Our focus in this chapter will be on iterative algorithmsfor solving (10.1). Chap. 10.1 describes various properties of saddle point systems. Chap. 10.2 introduces the dualityformulation and Uzawa's algorithm. Chap. 10.3 describes the penalty and regularizationmethod for obtaining an approximate solution. Chap. 10.4 describes projection methods. Chap. 10.5 describes block matrixpreconditioners and Krylov algorithms. Applications to Navier-Stokes equations, mixed formulations of elliptic equations, and to optimal control problems, are described in Chaps. 10.6, 10.7 and 10.8, respectively. For a more detailed discussion of saddle point problems, readers are referred to [CI4, GI3, BE12].