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

DOI:
https://doi.org/10.1090/S0025-5718-99-01090-X

Published electronically:
February 23, 1999

MathSciNet review:
1648371

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-99-01090-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