Unconditional stability and error estimates of modified characteristics FEMs for the Navier–Stokes equations
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
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Detail(s)
Original language | English |
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Pages (from-to) | 139-161 |
Journal / Publication | Numerische Mathematik |
Volume | 134 |
Issue number | 1 |
Online published | 26 Oct 2015 |
Publication status | Published - Sep 2016 |
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Abstract
The paper is concerned with the unconditional stability and convergence of characteristics type methods for the time-dependent Navier–Stokes equations. We present optimal error estimates in L2 and H1 norms for a typical modified characteristics finite element method unconditionally, while all previous works require certain time-step restrictions. The analysis is based on an iterated characteristic time-discrete system, with which the error function is split into a temporal error and a spatial error. With a rigorous analysis to the characteristic time-discrete system, we prove that the difference between the numerical solution and the solution of the time-discrete system is τ-independent, where τ denotes the time stepsize. Thus numerical solution in W1,∞ is bounded and optimal error estimates can be obtained in a traditional way. Numerical results confirm our analysis and show clearly the unconditional stability and convergence of the modified characteristics finite element method for the time-dependent Navier–Stokes equations. The approach used in this paper can be easily extended to many other characteristics-based methods.
Citation Format(s)
Unconditional stability and error estimates of modified characteristics FEMs for the Navier–Stokes equations. / Si, Zhiyong; Wang, Jilu; Sun, Weiwei.
In: Numerische Mathematik, Vol. 134, No. 1, 09.2016, p. 139-161.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review