Paper Info
Title
Finite volume element approximations of nonlocal in time one-dimensional flows in porous media
Abstract
Various finite volume element schemes for parabolic integro-differential equations in 1-D are derived and studied. These types of equations arise in modeling reactive flows or material with memory effects. Our main goal is to develop a general framework for obtaining finite volume element approximations and to study the error analysis. We consider the lowest-order (linear and L-splines) finite volume elements, although higher-order volume elements can be considered as well under this framework. It is proved that finite volume element approximations are convergent with optimal order in H 1-norms, suboptimal order in the L 2-norm and super-convergent order in a discrete H 1-norm.
Year
DOI
Venue
2000
10.1007/s006070050007
Computing
Keywords
DocType
Volume
AMS Subject Classifications: 65M12,65M60,65N40.,Key Words: Finite volume method,parabolic equation,integro-differential equation.
Journal
64
Issue
ISSN
Citations 
2
0010-485X
12
PageRank 
References 
Authors
2.26
0
3
Name
Order
Citations
PageRank
Richard E. Ewing125245.87
Raytcho D. Lazarov245682.23
Yanping Lin324426.94