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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A general mixed covolume framework
for constructing conservative schemes
for elliptic problems


Authors: So-Hsiang Chou and Panayot S. Vassilevski
Journal: Math. Comp. 68 (1999), 991-1011
MSC (1991): Primary 65F10, 65N20, 65N30
Published electronically: February 23, 1999
MathSciNet review: 1648371
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Abstract: We present a general framework for the finite volume or covolume schemes developed for second order elliptic problems in mixed form, i.e., written as first order systems. We connect these schemes to standard mixed finite element methods via a one-to-one transfer operator between trial and test spaces. In the nonsymmetric case (convection-diffusion equation) we show one-half order convergence rate for the flux variable which is approximated either by the lowest order Raviart-Thomas space or by its image in the space of discontinuous piecewise constants. In the symmetric case (diffusion equation) a first order convergence rate is obtained for both the state variable (e.g., concentration) and its flux. Numerical experiments are included.


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Additional Information

So-Hsiang Chou
Affiliation: Department of Mathematics, Bowling Green State University, Bowling Green, Ohio 43403, U.S.A.
Email: chou@zeus.bgsu.edu

Panayot S. Vassilevski
Affiliation: Center of Informatics and Computing Technology, Bulgarian Academy of Sciences, “Acad. G. Bontchev” street, Block 25 A, 1113 Sofia, Bulgaria
Email: panayot@iscbg.acad.bg

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01090-X
PII: S 0025-5718(99)01090-X
Keywords: Conservative schemes, mixed finite elements, covolume methods, finite volume methods, finite volume element, Raviart--Thomas spaces, error estimates, $H(\mydiv)$-preconditioning
Received by editor(s): June 16, 1997
Published electronically: February 23, 1999
Additional Notes: The work of the second author was partially supported by the Bulgarian Ministry for Education, Science and Technology under grant I–95 # 504
Article copyright: © Copyright 1999 American Mathematical Society