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Finite volume element approximations of nonlocal reactive flows in porous media

✍ Scribed by Richard Ewing; Raytcho Lazarov; Yanping Lin

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
234 KB
Volume
16
Category
Article
ISSN
0749-159X

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✦ Synopsis

In this article, we study finite volume element approximations for two-dimensional parabolic integrodifferential equations, arising in the modeling of nonlocal reactive flows in porous media. These types of flows are also called NonFickian flows and exhibit mixing length growth. For simplicity, we consider only linear finite volume element methods, although higher-order volume elements can be considered as well under this framework. It is proved that the finite volume element approximations derived are convergent with optimal order in H 1 -and L 2 -norm and are superconvergent in a discrete H 1 -norm. By examining the relationship between finite volume element and finite element approximations, we prove convergence in L ∞ -and W 1,∞ -norms. These results are also new for finite volume element methods for elliptic and parabolic equations.

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