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The stabilized Gauge-Uzawa method (SGUM), which is a second order projection type algorithm

to solve the time-dependent Navier-Stokes equations, has been newly constructed in

2013 Pyo's paper. The accuracy of SGUM has been proved only for time

discrete scheme in the same paper,

but it is crucial to study for fully discrete scheme,

because the numerical errors depend on discretizations for both space

and time,

and because discrete spaces between velocity and pressure can not be

chosen arbitrary.

In this paper, we find out properties of the fully discrete SGUM and

estimate its errors and stability to solve the evolution Navier-Stokes equations.

The main difficulty in this estimation arises from losing some cancellation laws

due to failing divergence free condition of the discrete velocity function.

This result will be extended to Boussinesq equations in the continuous research (part II)

and is essential in the study of part II.

권호기사

권호기사 목록 테이블로 기사명, 저자명, 페이지, 원문, 기사목차 순으로 되어있습니다.
기사명 저자명 페이지 원문 목차
Fuzzy connections and completeness in complete residuated lattices Yong Chan Kim, Young Sun Kim pp.101-116

Nontrivial solution for the biharmonic boundary value problem with some nonlinear term Tacksun Jung, Q-Heung Choi pp.117-124

Error estimates for the fully discrete stabilized Gauge-Uzawa method. part1, The Navier-Stokes equations Jae-Hong Pyo pp.125-150

The λ-number of the Cartesian product of a complete graph and a cycle Byeong Moon Kim, Byung Chul Song, Yoomi Rho pp.151-159

Approximate bi-homomorphisms and bi-derivations in C*-ternary algebras : revisited Young Cho, Sun Young Jang, Su Min Kwon, Choonkil Park, Won-Gil Park pp.161-170

Fuzzy semigroups in reductive semigroups Inheung Chon pp.171-180

A homomorphism of pointed minimal sets and quasi-Ellis groups Hyung-Soo Song pp.181-187

A study on the Cartesian closed category PosM Ig Sung Kim pp.189-195

A simple proof of Hilbert basis theorem for *_w_-Noetherian domains Jung Wook Lim, Dong Yeol Oh pp.197-201

Multiplicity results for the wave system using the linking theorem Hyewon Nam pp.203-212

참고문헌 (19건) : 자료제공( 네이버학술정보 )

참고문헌 목록에 대한 테이블로 번호, 참고문헌, 국회도서관 소장유무로 구성되어 있습니다.
번호 참고문헌 국회도서관 소장유무
1 S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods Springer-Verlag, (1994). 미소장
2 F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer- Verlag, (1991). 미소장
3 Numerical Solution of the Navier-Stokes Equations 네이버 미소장
4 P. Constantin and C. Foias, Navier-Stokes Equations, The University of Chicago Press (1988). 미소장
5 V. Girault, and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag (1986). 미소장
6 A new class of truly consistent splitting schemes for incompressible flows 네이버 미소장
7 J.L. Guermond and J. Shen On the error estimates of rotational pressurecorrection projection methods, Math. Comp., 73 (2004), 1719–1737. 미소장
8 Finite Element Approximation of the Nonstationary Navier-Stokes Problem. I. Regularity of Solutions and Second-Order Error Estimates for Spatial Discretization 네이버 미소장
9 K. Ito and Z. Qiao A high order compact MAC finite difference scheme for the Stokes equations: augmented variable approach, J. Comput. Phys., 227 (2008), 8177–8190. 미소장
10 A regularity result for the Stokes problem in a convex polygon 네이버 미소장
11 R.H. Nochetto and J.-H. Pyo, A finite element Gauge-Uzawa method. Part I : the Navier-Stokes equations, SIAM J. Numer. Anal., 43 (2005), 1043–1068. 미소장
12 R.H. Nochetto and J.-H. Pyo, A finite element Gauge-Uzawa method. Part II : Boussinesq equations, Math. Models Methods Appl. Sci., 16 (2006), 1599–1626. 미소장
13 A. Prohl, Projection and Quasi-Compressiblity Methods for Solving the Incompressible Navier-Stokes Equations, B.G.Teubner Stuttgart (1997). 미소장
14 J.-H. Pyo Error estimates for the second order semi-discrete stabilized Gauge- Uzawa method For the Navier-Stokes equations, Inter. J. Numer. Anal. and Model, 10 (2013), 24–41. 미소장
15 Normal mode analysis of second-order projection methods for incompressible flows 네이버 미소장
16 Gauge-Uzawa methods for incompressible flows with variable density 네이버 미소장
17 Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (II) 네이버 미소장
18 R. Temam, Navier-Stokes Equations, AMS Chelsea Publishing, (2001). 미소장
19 An Approximate Projection Scheme for Incompressible Flow using Spectral Elements 네이버 미소장

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