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Zbl 0646.76036
Heywood, John G.; Rannacher, Rolf
Finite element approximation of the nonstationary Navier-Stokes problem. III: Smoothing property and higher order error estimates for spatial discretization. (English)
[J] SIAM J. Numer. Anal. 25, No.3, 489-512 (1988). ISSN 0036-1429; ISSN 1095-7170/e

Summary: [For part II see the authors, ibid. 23, 750-777 (1986; Zbl 0611.76036).] \par This paper continues our error analysis of finite element Galerkin approximation of the nonstationary Navier-Stokes equations. Optimal order error estimates, both local and global, are derived for higher order finite elements under appropriate assumptions about the smoothness and stability of the solution. These assumptions take into account the loss of regularity at $t=0$ that one generally has to expect in the absence of higher order nonlocal compatibility conditions for the data of the problem.

MSC 2000:: *76D05 Navier-Stokes equations (fluid dynamics)
65N30 Finite numerical methods (BVP of PDE)
35Q30 Stokes and Navier-Stokes equations

Keywords: error analysis; finite element Galerkin approximation; nonstationary Navier-Stokes equations; Optimal order error estimates; smoothness; stability

Citations: Zbl 0487.76035; Zbl 0611.76036

Cited in: Zbl 1166.65381 Zbl 0694.76014

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