| Title:
|
Numerical analysis of the Navier-Stokes equations (English) |
| Author:
|
Rannacher, Rolf |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
1993 |
| Pages:
|
361-380 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper discusses some conceptional questions of the numerical simulation of viscous incompressible flow which are related to the presence of boundaries. (English) |
| Keyword:
|
incompressibility constraint |
| Keyword:
|
Chorin’s projection method |
| Keyword:
|
boundary conditions |
| Keyword:
|
well-posedness |
| Keyword:
|
nonlinear Galerkin method |
| MSC:
|
65M60 |
| MSC:
|
76D05 |
| MSC:
|
76M10 |
| MSC:
|
76M25 |
| idZBL:
|
Zbl 0798.76041 |
| idMR:
|
MR1228513 |
| DOI:
|
10.21136/AM.1993.104560 |
| . |
| Date available:
|
2008-05-20T18:46:11Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104560 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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[9] Gresho P. M.: Some current CFD issues relevant to the incompressible Navier-Stokes equations.Соmр. Meth. Appl. Mech. Eng. 87(1991), 201-252. Zbl 0760.76018, MR 1118944, 10.1016/0045-7825(91)90006-R |
| Reference:
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[10] Harig J.: A 3-d finite element upwind approximation of the stationary Navier Stokes equations.IWR-Report, Universität Heidelberg, 1991. |
| Reference:
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| Reference:
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[12] Heywood J .G., R. Rannacher: Finite element approximation of the nonstationary Navier-Stokes problem. Part 1: regularity of solutions and second-order error estimates for spatial discretization.SIAM J. Numer. Anal 19 (1982), 275-311 MR 0650052, 10.1137/0719018 |
| Reference:
|
[12b] Heywood J. G., R. Rannacher: Finite element approximation of the nonstationary Navier-Stokes problem. Part 2: Stability of solutions and error estimates uniform in time.ibidem 23, (1986), 750-777 MR 0849281 |
| Reference:
|
[12c] Heywood J.G., R. Rannacher: Finite element approximation of the nonstationary Navier-Stokes problem. Part 3: Smoothing property and higher order error estimates for spatial discretization.ibidem 25 (1988), 489-512 MR 0942204 |
| Reference:
|
[12d] Heywood J.G., R. Rannacher: Finite element approximation of the nonstationary Navier-Stokes problem. Part 4: error analysis for second-order time discretization.ibidem 27 (1990), 353-384. MR 1043610 |
| Reference:
|
[13] Heywood J. G., Rannacher R., and S.Turek: Artifical boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations.Universität Heidelberg, April 1992, Preprint. MR 1380844 |
| Reference:
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[14] Heywood J. G., R. Rannacher: On the question of turbulence modeling by approximate inertial manifolds and the nonlinear Galerkin method.Universität Heidelberg, May 1992, Preprint. MR 1249035 |
| Reference:
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[15] Hughes T. J. R., Franca L. P., and M. Balestra: A new finite element formulation for computational fluid mechanics: V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommoding equal order interpolation.Соmр. Meth. Appl. Mech. Eng. 59 (1986), 85-99. MR 0868143, 10.1016/0045-7825(86)90025-3 |
| Reference:
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[16] Kracmar S., and J. Neustupa: Global existence of weak solutions of a nonstationary variational inequality of the Navier-Stokes type with mixed boundary conditions.Dept. of Techn. Math., Czech Techn. Univ, Praha, 1992, Preprint. |
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[17] Marion M., and R. Temam: Nonlinear Galerkin methods: The finite element case.Numer. Math. 57, (1990), 205-226. MR 1057121, 10.1007/BF01386407 |
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|
[18] Prohl A., and R. Rannacher: On some pseudo-compressibility methods for the Navier-Stokes equations.in preparation. |
| Reference:
|
[19] Rannacher R.: Numerical analysis of nonstationary fluid flow (a survey).In: Applications of Mathematics in Industry and Technology (V. C. Boffi and H. Neunzert, eds.), Teubner, Stuttgart, 1989, pp. 34-53. MR 1079942 |
| Reference:
|
[20] Rannacher R.: On Chorin's projection method for the incompressible Navier-Stokes equations.Springer, (R. Rautmann, et.al., eds.), Proc. Oberwolfach Conf., 19.-23. 8. 1991. |
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|
[21] Rannacher R., and S. Turek: Simple nonconforming quadrilateral Stokes elements.Numer. Meth. Part. Diff. Equ. 8 (1992), 97-111. MR 1148797, 10.1002/num.1690080202 |
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