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A new Bramble-Pasciak-like preconditioner for saddle point problems

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  • A new Bramble-Pasciak-like preconditioner with parameter is proposed for solving a linear system in the saddle point form. The system can be reformulated as a symmetric positive definite system with respect to some inner product and thus can be solved by the Bramble-Pasciak conjugate gradient (BPCG) method. Based on the spectral condition number of the associated system, the quasi-optimal parameters can be obtained to improve the convergence rate of the BPCG method. Numerical experiments on the Stokes problem are given to illustrate our theoretical results.
    Mathematics Subject Classification: Primary: 65F10, 65F15.


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