Summary
The finite element discretization of many elliptic boundary value problems leads to linear systems with positive definite and symmetric coefficient matrices. Many efficient preconditioners are known for these systems. We show that these preconditioning matrices can also be used for the linear systems arising from boundary value problems which are potentially indefinite due to lower order terms in the partial differential equation. Our main tool is a careful algebraic analysis of the condition numbers and the spectra of perturbed matrices which are preconditioned by the same matrices as in the unperturbed case.
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Yserentant, H. Preconditioning indefinite discretization matrices. Numer. Math. 54, 719–734 (1989). https://doi.org/10.1007/BF01396490
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DOI: https://doi.org/10.1007/BF01396490