Algebraic Aspects of Saddle Point Problems

Abstract

The examples of Chap. 1 clearly showed that several formulations typically lead to linear systems of the general form

$$\displaystyle{ \left (\begin{array}{lll} &A\quad &{B}^{T} \\ &B\quad &0 \end{array} \right )\left (\begin{array}{l} \mathbf{x}\\ \mathbf{y} \end{array} \right ) = \left (\begin{array}{l} \mathbf{f}\\ \mathbf{g} \end{array} \right ), }$$

(3.0.1)

where A and B are linear differential operators from some functional space to another (which often is its dual space).