zbMATH — the first resource for mathematics

Higher-order finite element discretizations in a benchmark problem for incompressible flows. (English) Zbl 1007.76040
From the summary: We present a numerical study of several finite element discretizations applied to a benchmark problem for the two-dimensional steady incompressible Navier Stokes equations. The discretizations are compared with respect to the accuracy of computed benchmark parameters. Higher-order isoparametric finite element discretizations turned out to be by far the most accurate. The discrete systems obtained with higher-order discretizations are solved with a modified coupled multigrid method whose behaviour within the benchmark problem is also studied numerically.

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI
[1] The benchmark problem ?Flow around a cylinder?. In Flow Simulation with High-Performance Computers II. Notes on Numerical Fluid Mechanics, vol. 52, (ed.). Vieweg: Wiesbaden, 1996; 547-566.
[2] Finite Element Methods for Navier-Stokes Equations. Springer: Berlin, 1986. · Zbl 0585.65077 · doi:10.1007/978-3-642-61623-5
[3] Parallele Lösung der inkompressiblen Navier-Stokes Gleichungen auf adaptiv verfeinerten Gittern. PhD thesis, Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, 1997.
[4] Rannacher, Numerical Methods for Partial Differential Equations 8 pp 97– (1992) · Zbl 0742.76051 · doi:10.1002/num.1690080202
[5] Parallele Lösung der stationären inkompressiblen Navier-Stokes Gleichungen. Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Habilitation, 1997.
[6] Mixed and hybrid finite element methods. In Springer Series in Computational Mathematics, vol. 15. Springer: Berlin, 1991. · Zbl 0788.73002 · doi:10.1007/978-1-4612-3172-1
[7] Fortin, Acta Numerica pp 239– (1993) · doi:10.1017/S0962492900002373
[8] A multidimensional upwind scheme with no crosswind diffusion. In Finite Element Methods for Convection Dominated Flows, AMD, vol. 34, (ed.). ASME: New York, 1979; 19-35.
[9] Brooks, Computer Methods in Applied Mechanics and Engineering 32 pp 199– (1982) · Zbl 0497.76041 · doi:10.1016/0045-7825(82)90071-8
[10] Lube, Journal of Computational Mathematics 8 pp 147– (1990)
[11] Tobiska, SIAM Journal of Numerical Analysis 33 pp 107– (1996) · Zbl 0843.76052 · doi:10.1137/0733007
[12] Schieweck, Numerical Methods for Partial Differential Equations 12 pp 407– (1996) · Zbl 0856.76037 · doi:10.1002/(SICI)1098-2426(199607)12:4<407::AID-NUM1>3.0.CO;2-Q
[13] Vanka, Computer Methods in Applied Mechanics and Engineering 59 pp 29– (1986) · Zbl 0604.76025 · doi:10.1016/0045-7825(86)90022-8
[14] Efficient solvers for incompressible flow problems: an algorithmic and computational approach. In Lecture Notes in Computational Science and Engineering, vol. 6. Springer: Berlin, 1999. · doi:10.1007/978-3-642-58393-3
[15] John, Computing and Visualization in Science 4 pp 193– (1999) · Zbl 1015.76072 · doi:10.1007/s007910050018
[16] John, International Journal for Numerical Methods in Fluids 33 pp 453– (2000) · Zbl 0979.76047 · doi:10.1002/1097-0363(20000630)33:4<453::AID-FLD15>3.0.CO;2-0
[17] A comparison of three solvers for the incompressible Navier-Stokes equations. In Large-Scale Scientific Computations of Engineering and Environmental Problems. Notes on Numerical Fluid Mechanics, vol. 73, (eds). Vieweg: Wiesbaden, 2000; 215-222. · Zbl 0985.76053
[18] A general transfer operator for arbitrary finite element spaces. Preprint 25, Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, 2000.
[19] Weighted error estimators for finite element approximations of the incompressible Navier-Stokes equations. Universität Heidelberg. Preprint 48/98, 1998.
[20] Weighted a posteriori error control in fe methods. In ENUMATH 97, Proceedings of the 2nd European Conference on Numerical Mathematics and Advanced Applications, et al. (eds). World Scientific Publishing Company: Singapore, 1996; 621-637.
[21] MooNMD2.2. Otto-von-Guericke-Universität Magdeburg, Institut für Analysis und Numerik, 2001.
[22] On higher order methods for the stationary incompressible Navier-Stokes equations. PhD thesis, Universität Heidelberg. Preprint 42/98, 1998.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.