Finite volume element approximations of nonlocal in time one-dimensional plows in porous media Academic Article

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 H1-norms, suboptimal order in the L2-norm and super-convergent order in a discrete H1-norm.

authors

• Lazarov, Raytcho

published proceedings

• COMPUTING

author list (cited authors)

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

citation count

• 34

complete list of authors

• Ewing, RE||Lazarov, RD||Lin, YP

publication date

• January 2000

publisher

• Springer Nature  Publisher

published in

• Computing  Journal

keywords

• Finite Volume Method
• Integro-differential Equation
• Parabolic Equation

Digital Object Identifier (DOI)

• 10.1007/s006070050007

start page

• 157

end page

• 182

volume

• 64

issue

• 2

URL

• http://dx.doi.org/10.1007/s006070050007