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Volume 22, Issue 5
The Upwind Finite Element Scheme and Maximum Principle for Nonlinear Convection-Diffusion Problem

Zhiyong Zhao & Jianwei Hu

J. Comp. Math., 22 (2004), pp. 699-718.

Published online: 2004-10

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  • Abstract

In this paper, a kind of partial upwind finite element scheme is studied for two-dimensional nonlinear convection-diffusion problem. Nonlinear convection term approximated by partial upwind finite element method considered over a mesh dual to the triangular grid, whereas the nonlinear diffusion term approximated by Galerkin method. A linearized partial upwind finite element scheme and a higher order accuracy scheme are constructed respectively. It is shown that the numerical solutions of these schemes preserve discrete maximum principle. The convergence and error estimate are also given for both schemes under some assumptions. The numerical results show that these partial upwind finite element schemes are feasible and accurate.

  • Keywords

Convection-diffusion problem, Partial upwind finite element, Maximum principle.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-699, author = {Zhao , Zhiyong and Hu , Jianwei}, title = {The Upwind Finite Element Scheme and Maximum Principle for Nonlinear Convection-Diffusion Problem}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {5}, pages = {699--718}, abstract = {

In this paper, a kind of partial upwind finite element scheme is studied for two-dimensional nonlinear convection-diffusion problem. Nonlinear convection term approximated by partial upwind finite element method considered over a mesh dual to the triangular grid, whereas the nonlinear diffusion term approximated by Galerkin method. A linearized partial upwind finite element scheme and a higher order accuracy scheme are constructed respectively. It is shown that the numerical solutions of these schemes preserve discrete maximum principle. The convergence and error estimate are also given for both schemes under some assumptions. The numerical results show that these partial upwind finite element schemes are feasible and accurate.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10297.html} }
TY - JOUR T1 - The Upwind Finite Element Scheme and Maximum Principle for Nonlinear Convection-Diffusion Problem AU - Zhao , Zhiyong AU - Hu , Jianwei JO - Journal of Computational Mathematics VL - 5 SP - 699 EP - 718 PY - 2004 DA - 2004/10 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10297.html KW - Convection-diffusion problem, Partial upwind finite element, Maximum principle. AB -

In this paper, a kind of partial upwind finite element scheme is studied for two-dimensional nonlinear convection-diffusion problem. Nonlinear convection term approximated by partial upwind finite element method considered over a mesh dual to the triangular grid, whereas the nonlinear diffusion term approximated by Galerkin method. A linearized partial upwind finite element scheme and a higher order accuracy scheme are constructed respectively. It is shown that the numerical solutions of these schemes preserve discrete maximum principle. The convergence and error estimate are also given for both schemes under some assumptions. The numerical results show that these partial upwind finite element schemes are feasible and accurate.

Zhao , Zhiyong and Hu , Jianwei. (2004). The Upwind Finite Element Scheme and Maximum Principle for Nonlinear Convection-Diffusion Problem. Journal of Computational Mathematics. 22 (5). 699-718. doi:
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