论文信息 - A Note on the Consistency and Stability Properties of Yosida Fractional Step Schemes for the Unsteady Stokes Equations

A Note on the Consistency and Stability Properties of Yosida Fractional Step Schemes for the Unsteady Stokes Equations

In this short note we give some improvements to the stability and consistency analysis of algebraic splitting methods for solving the incompressible fluid equations carried out in [P. Gervasio, SIAM J. Numer. Anal., 46 (2008), pp. 1682-1703]. In particular, we generalize to any value of the approximation index $p\in\mathbb{N}$ Proposition 3.1 and Lemma 3.2 of [P. Gervasio, SIAM J. Numer. Anal., 46 (2008), pp. 1682-1703] on the consistency error associated with the algebraic splitting, originally proved for $p=0,1,2$. Moreover, we remove an assumption of Lemma 3.5 of [P. Gervasio, SIAM J. Numer. Anal., 46 (2008), pp. 1682-1703].

Alessandro Veneziani

[1] A. Veneziani. Block factorized preconditioners for high‐order accurate in time approximation of the Navier‐Stokes equations , 2003 .

[2] Alfio Quarteroni,et al. Analysis of the Yosida Method for the Incompressible Navier-Stokes Equations , 1999 .

[3] Paola Gervasio,et al. Convergence Analysis of High Order Algebraic Fractional Step Schemes for Time-Dependent Stokes Equations , 2008, SIAM J. Numer. Anal..

[4] Alessandro Veneziani,et al. Pressure Correction Algebraic Splitting Methods for the Incompressible Navier-Stokes Equations , 2005, SIAM J. Numer. Anal..

[5] A. Quarteroni,et al. Factorization methods for the numerical approximation of Navier-Stokes equations , 2000 .

[6] Paola Gervasio,et al. Algebraic fractional-step schemes with spectral methods for the incompressible Navier-Stokes equations , 2006, J. Comput. Phys..

[7] A. Quarteroni,et al. Numerical Approximation of Partial Differential Equations , 2008 .