Volume 23, Issue 5
An Expanded Characteristic-Mixed Finite Element Method

Ling Guo & Huan-Zhen Chen

DOI:

J. Comp. Math., 23 (2005), pp. 479-490

Published online: 2005-10

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  • Abstract

In this paper, we propose an Expanded Characteristic-mixed Finite Element Method for approximating the solution to a convection dominated transport problem. The method is a combination of characteristic approximation to handle the convection part in time and an expanded mixed finite element spatial approximation to deal with the diffusion part. The scheme is stable since fluid is transported along the approximate characteristics on the discrete level. At the same time it expands the standard mixed finite element method in the sense that three variables are explicitly treated: the scalar unknown, its gradient, and its flux. Our analysis shows the method approximates the scalar unknown, its gradient, and its flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. A numerical example is presented to show that the scheme is of high performance.

  • Keywords

Convection diffusion problems Expanded characteristic mixed finite element method Optimal error estimates Numerical test

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COPYRIGHT: © Global Science Press

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@Article{JCM-23-479, author = {}, title = {An Expanded Characteristic-Mixed Finite Element Method}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {5}, pages = {479--490}, abstract = { In this paper, we propose an Expanded Characteristic-mixed Finite Element Method for approximating the solution to a convection dominated transport problem. The method is a combination of characteristic approximation to handle the convection part in time and an expanded mixed finite element spatial approximation to deal with the diffusion part. The scheme is stable since fluid is transported along the approximate characteristics on the discrete level. At the same time it expands the standard mixed finite element method in the sense that three variables are explicitly treated: the scalar unknown, its gradient, and its flux. Our analysis shows the method approximates the scalar unknown, its gradient, and its flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. A numerical example is presented to show that the scheme is of high performance. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8833.html} }
TY - JOUR T1 - An Expanded Characteristic-Mixed Finite Element Method JO - Journal of Computational Mathematics VL - 5 SP - 479 EP - 490 PY - 2005 DA - 2005/10 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8833.html KW - Convection diffusion problems KW - Expanded characteristic mixed finite element method KW - Optimal error estimates KW - Numerical test AB - In this paper, we propose an Expanded Characteristic-mixed Finite Element Method for approximating the solution to a convection dominated transport problem. The method is a combination of characteristic approximation to handle the convection part in time and an expanded mixed finite element spatial approximation to deal with the diffusion part. The scheme is stable since fluid is transported along the approximate characteristics on the discrete level. At the same time it expands the standard mixed finite element method in the sense that three variables are explicitly treated: the scalar unknown, its gradient, and its flux. Our analysis shows the method approximates the scalar unknown, its gradient, and its flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. A numerical example is presented to show that the scheme is of high performance.
Ling Guo & Huan-Zhen Chen. (1970). An Expanded Characteristic-Mixed Finite Element Method. Journal of Computational Mathematics. 23 (5). 479-490. doi:
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