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Wu, J.; Zhu, J. Z.; Szmelter, J.; Zienkiewicz, O. C.

Error estimation and adaptivity in Navier-Stokes incompressible flows. (English) Zbl 0699.76035

Comput. Mech. 6, No. 4, 259-270 (1990).
Summary: An adaptive remeshing procedure for solving Navier-Stokes incompressible fluid flow problems is presented in this paper. This procedure has been implemented using the error estimator developed by the second and the fourth author [e.g. in Int. J. Numer. Methods Eng. 24, 337-357 (1987; Zbl 0602.73063)] and a semi-implicit time-marching scheme for Navier- Stokes flow problems [the third and the fourth author with J. Peraire in Comput. Methods Appl. Mech. Eng. 78, No.1, 105-121 (1990)]. Numerical examples are presented, showing that the error estimation and adaptive procedure are capable of monitoring the flow field, updating the mesh when necessary, and providing nearly optimal meshes throughout the calculation, thus making the solution reliable and the computation economical and efficient.

Cited in 32 Documents

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
65N99 Numerical methods for partial differential equations, boundary value problems

Keywords:

adaptive remeshing procedure; Navier-Stokes incompressible fluid flow problems

Citations:

Zbl 0602.73063
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Full Text: DOI

References:

[1] Ainsworth, M.; Zhu, J. Z.; Craig, A. W.; Zienkiewicz, O. C. (1989): Analysis of the Zienkiewicz-Zhu a-posteriori error estimator in the finite element method. Int. J. Numer. Meth. Engg. 28, 2161-2174 · Zbl 0716.73082 · doi:10.1002/nme.1620280912
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[11] Zienkiewicz, O. C.; Zhu, J. Z. (1987): A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Meth. Engg. 24, 337-357 · Zbl 0602.73063 · doi:10.1002/nme.1620240206
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[13] Zienkiewicz, O. C.; Taylor, R. L. (1989): The finite element method, 4-th ed., Vol. 1. New York: McGraw-Hill
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