ISSN:
1436-5057
Keywords:
AMS Subject Classifications: 65M12, 65M60, 65N40.
;
Key Words: Finite volume method, parabolic equation, integro-differential equation.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s006070050007
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