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.
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Received August 3, 1998; revised October 11, 1999
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Ewing, R., Lazarov, R. & Lin, Y. Finite Volume Element Approximations of Nonlocal in Time One-Dimensional Flows in Porous Media. Computing 64, 157–182 (2000). https://doi.org/10.1007/s006070050007
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DOI: https://doi.org/10.1007/s006070050007