Volume 5, Issue 2
A Mixed Stiffness Finite Element Method for Navier-Stokes Equation

Wu Zhang & Tian-Xiao Zhou

DOI:

J. Comp. Math., 5 (1987), pp. 156-180

Published online: 1987-05

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  • Abstract

The paper is devoted to the study and analysis of the mixed stiffness finite elment method for the Navier-Stokes equations, based on a formulation of velocity-pressure-stress deviatorics. The method used low order Lagrange elementsm and leads to optimal error order of convergence for velocity, pressure, and stress deviatirics by means of mesh-dependent norms defined in this paper. The main advantage of the MSFEN is that the streafunction can not only be employed to satisfy the divergence constraint but stress deviatorics can also be eliminated at the lement level so that it is unnecessary to solve a larger algebraic system containing stress multiplies, or to develop a special code for computing the MSFE soltuiongs of Navier-stokes equations because we can use the computing codes used in solving the Navier-stokes equations with the velocity-pressure formulation, or even the computing codes used in solving the problems of solid mechanics.

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@Article{JCM-5-156, author = {Wu Zhang and Tian-Xiao Zhou}, title = {A Mixed Stiffness Finite Element Method for Navier-Stokes Equation}, journal = {Journal of Computational Mathematics}, year = {1987}, volume = {5}, number = {2}, pages = {156--180}, abstract = { The paper is devoted to the study and analysis of the mixed stiffness finite elment method for the Navier-Stokes equations, based on a formulation of velocity-pressure-stress deviatorics. The method used low order Lagrange elementsm and leads to optimal error order of convergence for velocity, pressure, and stress deviatirics by means of mesh-dependent norms defined in this paper. The main advantage of the MSFEN is that the streafunction can not only be employed to satisfy the divergence constraint but stress deviatorics can also be eliminated at the lement level so that it is unnecessary to solve a larger algebraic system containing stress multiplies, or to develop a special code for computing the MSFE soltuiongs of Navier-stokes equations because we can use the computing codes used in solving the Navier-stokes equations with the velocity-pressure formulation, or even the computing codes used in solving the problems of solid mechanics. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9540.html} }
TY - JOUR T1 - A Mixed Stiffness Finite Element Method for Navier-Stokes Equation AU - Wu Zhang & Tian-Xiao Zhou JO - Journal of Computational Mathematics VL - 2 SP - 156 EP - 180 PY - 1987 DA - 1987/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9540.html KW - AB - The paper is devoted to the study and analysis of the mixed stiffness finite elment method for the Navier-Stokes equations, based on a formulation of velocity-pressure-stress deviatorics. The method used low order Lagrange elementsm and leads to optimal error order of convergence for velocity, pressure, and stress deviatirics by means of mesh-dependent norms defined in this paper. The main advantage of the MSFEN is that the streafunction can not only be employed to satisfy the divergence constraint but stress deviatorics can also be eliminated at the lement level so that it is unnecessary to solve a larger algebraic system containing stress multiplies, or to develop a special code for computing the MSFE soltuiongs of Navier-stokes equations because we can use the computing codes used in solving the Navier-stokes equations with the velocity-pressure formulation, or even the computing codes used in solving the problems of solid mechanics.
Wu Zhang & Tian-Xiao Zhou. (1970). A Mixed Stiffness Finite Element Method for Navier-Stokes Equation. Journal of Computational Mathematics. 5 (2). 156-180. doi:
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