Finite volume element approximations of nonlocal reactive flows in porous media Academic Article

abstract

• In this article, we study finite volume element approximations for two-dimensional parabolic integro-differential 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 H1- and L2-norm and are superconvergent in a discrete H1-norm. By examining the relationship between finite volume element and finite element approximations, we prove convergence in L- and W1,-norms. These results are also new for finite volume element methods for elliptic and parabolic equations. 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 285-311, 2000.

authors

• Lazarov, Raytcho

published proceedings

• NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

author list (cited authors)

• Ewing, R., Lazarov, R., & Lin, Y. P.

citation count

• 100

complete list of authors

• Ewing, R||Lazarov, R||Lin, YP

publication date

• May 2000

publisher

• Wiley  Publisher

published in

• Numerical Methods for Partial Differential Equations  Journal

keywords

• Control Volume
• Error Estimates
• Finite Volume Element
• Nonfickian Flows

Digital Object Identifier (DOI)

• 10.1002/(SICI)1098-2426(200005)16:3<285::AID-NUM2>3.0.CO;2-3

start page

• 285

end page

• 311

volume

• 16

issue

• 3

URL

• http://dx.doi.org/10.1002/(sici)1098-2426(200005)16:3%3C285::aid-num2%3E3.0.co;2-3