New Analysis of Galerkin FEMs for Miscible Displacement in Porous Media
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
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Detail(s)
Original language | English |
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Pages (from-to) | 903-923 |
Journal / Publication | Journal of Scientific Computing |
Volume | 80 |
Issue number | 2 |
Online published | 29 Apr 2019 |
Publication status | Published - Aug 2019 |
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Abstract
The paper is concerned with optimal error estimates of classical Galerkin FEMs for the equations of incompressible miscible flows in porous media. The analysis done in the last several decades shows that classical Galerkin FEMs provide the numerical concentration of the accuracy O (τk + hr+1 + hs) in L2-norm. This analysis leads to the use of higher order finite element approximation to the pressure than that to the concentration in various numerical simulations to achieve the best rate of convergence. However, this error estimate is not optimal. The purpose of this paper is to establish the optimal L2 error estimate O (τk + hr+1 + hs+1), from which one can see that the best convergence rate can be achieved by taking the same order (r = s) approximation to the concentration and pressure. Clearly Galerkin FEMs with r = s are less expensive in computation and easier for implementation. Numerical results for both two and three-dimensional models are presented to confirm our theoretical analysis.
Citation Format(s)
New Analysis of Galerkin FEMs for Miscible Displacement in Porous Media. / Wu, Chengda; Sun, Weiwei.
In: Journal of Scientific Computing, Vol. 80, No. 2, 08.2019, p. 903-923.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review