Spectral properties of primal-based penalty preconditioners for saddle point problems
A preconditioner for the system \[ \begin{pmatrix} A & B^T \cr B & -C \end{pmatrix} \begin{pmatrix} u \cr p \end{pmatrix} = b \] is obtained with an approximation \(\hat C\) of \(C\) and \(\hat S\) of the Schur complement \(S=A+B^T\hat C^{-1}B\). The method can be understood as follows: The matrix is rearranged \[ \begin{pmatrix} C & B \cr B^T & -A \end{pmatrix} \] and standard preconditioners are applied.
scientific article; zbMATH DE number 5669150
scientific article