Preconditioning of matrices partitioned in 2 × 2 block form: eigenvalue estimates and Schwarz DD for mixed FEM

A general framework for constructing preconditioners for 2 × 2 block matrices is presented, and eigenvalue bounds of the preconditioned matrices are derived. The results are applied both for positive-definite problems and for saddle point matrices of regularized forms. Eigenvalues and minimal polynomials for certain limit cases are derived. A domain decomposition method, with overlap, is used to solve the pivot block of the regularized matrix. Special attention is paid to problems with heterogeneous coefficients. Copyright © 2010 John Wiley & Sons, Ltd.

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