FOV-equivalent block triangular preconditioners for generalized saddle-point problems

We present sufficient conditions for field-of-values-equivalence between block triangular preconditioners and generalized saddle-point matrices arising from inf-sup stable finite element discretizations. We generalize a result by Loghin and Wathen (2004) for matrices with a pure saddle-point structure to the case where the (2,2) block is non-zero. Moreover, we extend the analysis to the case where the (2,1) block is not the transpose of the (1,2) block.