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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


New analysis of Galerkin-mixed FEMs for incompressible miscible flow in porous media
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by Weiwei Sun and Chengda Wu HTML | PDF
Math. Comp. 90 (2021), 81-102 Request permission


Analysis of Galerkin-mixed FEMs for incompressible miscible flow in porous media has been investigated extensively in the last several decades. Of particular interest in practical applications is the lowest-order Galerkin-mixed method, in which a linear Lagrange FE approximation is used for the concentration and the lowest-order Raviart-Thomas FE approximation is used for the velocity/pressure. The previous works only showed the first-order accuracy of the method in $L^2$-norm in spatial direction, which however is not optimal and valid only under certain extra restrictions on both time step and spatial mesh. In this paper, we provide new and optimal $L^2$-norm error estimates of Galerkin-mixed FEMs for all three components in a general case. In particular, for the lowest-order Galerkin-mixed FEM, we show unconditionally the second-order accuracy in $L^2$-norm for the concentration. Numerical results for both two- and three-dimensional models are presented to confirm our theoretical analysis. More important is that our approach can be extended to the analysis of mixed FEMs for many strongly coupled systems to obtain optimal error estimates for all components.
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Additional Information
  • Weiwei Sun
  • Affiliation: Advanced Institute of Natural Sciences, Beijing Normal University at Zhuhai, 519087, People’s Republic of China; and Division of Science and Technology, United International College (BNU-HKBU), Zhuhai, 519087, People’s Republic of China
  • Email:
  • Chengda Wu
  • Affiliation: Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, People’s Repubilic of China
  • MR Author ID: 1269306
  • Email:
  • Received by editor(s): September 12, 2018
  • Received by editor(s) in revised form: September 15, 2019, and February 12, 2020
  • Published electronically: September 8, 2020
  • Additional Notes: The research was supported in part by the Zhujiang Scholar program and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, People’s Republic of China (Project No. CityU 11302915).
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 81-102
  • MSC (2010): Primary 35K61, 65N12, 65N30
  • DOI:
  • MathSciNet review: 4166454