Weighted L2-stability of a discrete kinetic approximation for the incompressible Navier-Stokes equations on bounded domains

Abstract This paper is concerned with the stability of a discrete kinetic approximation with a boundary scheme introduced by the authors in a previous work. We prove the weighted L 2 -stability of the approximation by using an identity on three-point difference schemes for convection equations. With the weighted L 2 -stability, the convergence of the discrete kinetic approximation can be directly established. Moreover, the present stability analysis, particularly the identity on three-point difference schemes, may be adapted to other kinetic methods. Numerical experiments are conducted to verify our stability results.

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