PARAMETER-ROBUST PRECONDITIONING FOR OSEEN ITERATION APPLIED TO STATIONARY AND INSTATIONARY NAVIER-STOKES CONTROL PROBLEMS

Santolo Leveque, John W Pearson

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We derive novel, fast, and parameter-robust preconditioned iterative methods for steady and time-dependent Navier--Stokes control problems. Our approach may be applied to time-dependent problems which are discretized using backward Euler or Crank--Nicolson, and is also a valuable candidate for Stokes control problems discretized using Crank--Nicolson. The key ingredients of the solver are a saddle-point type approximation for the linear systems, an inner iteration for the (1,1)-block accelerated by a preconditioner for convection--diffusion control, and an approximation to the Schur complement based on a potent commutator argument applied to an appropriate block matrix. A range of numerical experiments validate the effectiveness of our new approach.
Original languageEnglish
Number of pages29
JournalSIAM Journal on Scientific Computing
Publication statusAccepted/In press - 13 Dec 2021

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