An Expanded Characteristic-Mixed Finite Element Method for a Convection-Dominated Transport Problem

An Expanded Characteristic-Mixed Finite Element Method for a Convection-Dominated Transport Problem

Year:    2005

Journal of Computational Mathematics, Vol. 23 (2005), Iss. 5 : pp. 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.  

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2005-JCM-8833

Journal of Computational Mathematics, Vol. 23 (2005), Iss. 5 : pp. 479–490

Published online:    2005-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

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